Bibliography of David B. Mumford
Algebraic Geometry
Books
[GIT] Geometric Invariant Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Band 34. Springer-Verlag, 1965, vi+145 pp. Second
enlarged edition (with J. Fogarty). 1982, xii+220 pp. Third enlarged edition
(with F. Kirwan and J. Fogarty). 1994, xiv+292 pp.
[CAS] Lectures on Curves on an Algebraic Surface (with a section by G.M.
Bergman). Annals of Mathematics Studies, No. 59. Princeton University
Press, Princeton, N.J., 1966, xi+200 pp.
[RB] Introduction to Algebraic Geometry: preliminary version of the first 3 chapters. Mimeographed notes from the Harvard Mathematics Department and
bound in red. Reprinted as The Red Book of Varieties and Schemes. Lecture Notes in Mathematics, 1358, Springer-Verlag, 1988, vi+309 pp; second
expanded edition, including the Ziwet Lectures at the University of Michigan (1974) on curves and their Jacobians (with contributions by Enrico Arbarello). 1999, x+306 pp.
[AV] Abelian Varieties. Tata Institute of Fundamental Research Studies in Mathematics, No. 5. Published for the Tata Institute of Fundamental Research,
Bombay; Oxford University Press, London, 1970, viii+242 pp. Second edition (with Appendices by C.P. Ramanujam and Y. Manin). 1974, x+279 pp.
Corrected reprint of the second edition. Hindustan Book Agency, New Delhi
(international distribution by the American Mathematical Society), 2008,
xii+263 pp.
[AS] Appendices to Algebraic Surfaces by O. Zariski, Second supplemented edition, on pages 71–74, 88–91, 118–128, 147–155, 197–206, 229–231, 238–
239 (with S.S. Abhyankar and J. Lipman). Ergebnisse der Mathematik und
ihrer Grenzgebiete, Band 61. Springer-Verlag, 1971, xi+270 pp.
[TE] Toroidal Embeddings I (with G. Kempf, F.F. Knudsen and B. Saint-Donat).
Lecture Notes in Mathematics, Vol. 339. Springer-Verlag, 1973, viii+209 pp.
xiii
xiv
Bibliography
[CJ]
Curves and their Jacobians. The University of Michigan Press, Ann Arbor,
Mich., 1975, vi+104 pp. Reprinted as an appendix (pp. 225–304) in the second expanded edition of [RB].
[SC] Smooth Compactification of Locally Symmetric Varieties (with A. Ash, M.
Rapoport and Y.-S. Tai). Lie Groups: History, Frontiers and Applications,
Vol. IV, Math. Sci. Press, Brookline, Mass., 1975, iv+335 pp.
[AG1] Algebraic Geometry I. Complex Projective Varieties. Grundlehren der Mathematischen Wissenschaften, No. 221. Springer-Verlag, 1976, x+186 pp.
Reprinted in the “Classics in Mathematics” series, Springer-Verlag, 1995,
x+186 pp.
[Θ 1] Tata Lectures on Theta I, containing Introduction and motivation: theta functions in one variable, Basic results on theta functions in several variables
(with the assistance of C. Musili, M. Nori, E. Previato and M. Stillman).
Progress in Mathematics, 28. Birkhäuser Boston, Inc., Boston, Mass, 1983,
xiii+235 pp. Republished in the Modern Birkhäuser Classics series, 2007.
[Θ 2] Tata Lectures on Theta II, Jacobian theta functions and differential equations (with the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman
and H. Umemura). Progress in Mathematics, 43. Birkhäuser Boston, Inc.,
Boston, Mass, 1984. xiv+272 pp. Republished in the Modern Birkhäuser
Classics series, 2007.
[Θ 3] Tata Lectures on Theta III (with the collaboration of M. Nori and P. Norman). Progress in Mathematics, 97. Birkhäuser Boston, Inc., Boston, Mass,
1991, viii+202 pp. Republished in the Modern Birkhäuser Classics series,
2007.
[SP1] Selected Papers on the Classification of Varieties and Moduli Spaces.
Springer-Verlag, 2004, xiii+795 pp.
Papers
[61a] The topology of normal singularities of an algebraic surface and a criterion
for simplicity. Publ. Math. de l’I.H.É.S. No. 9, 1961, 5–22.
[61b] Pathologies of modular algebraic surfaces. Amer. J. Math. 83, 1961, 339–
342.
[61c] An elementary theorem in geometric invariant theory. Bull. Amer. Math. Soc.
67, 1961, 483–487.
[62a] Further pathologies in algebraic geometry. Amer. J. Math. 84, 1962, 642–
648.
[62b] The canonical ring of an algebraic surface. An appendix to a paper by Oscar
Zariski, “The theorem of Riemann–Roch for high multiples of an effective
divisor on an algebraic surface, Ann. of Math. (2) 76, 1962, 560–615”, Ann.
of Math. (2) 76, 1962, 612–615.
[63a] Projective invariants of projective structures and applications. In Proc. Internat. Congr. Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm, 1963, 526–530.
Algebraic Geometry
xv
[63b] Some aspects of the problem of moduli (translated into Japanese by Y. Akizuki). Sûgaku 15, 1963/1964, 155–157.
[64] Two fundamental theorems on deformations of polarized varieties (with T.
Matsusaka). Amer. J. Math. 86, 1964, 668–684.
Correction to: “Two fundamental theorems on deformations of polarized varieties”. Amer. J. Math. 91, 1969, 851.
[65a] A remark on Mordell’s conjecture. Amer. J. Math. 87, 1965, 1007–1016.
[65b] Picard groups of moduli problems. In Arithmetical Algebraic Geometry,
(Proc. Conf. Purdue Univ., 1963), Harper & Row, New York, 1965, 33–81.
[66a] On the equations defining abelian varieties. I. Invent. Math. 1, 1966, 287–
354.
[66b] Families of abelian varieties. In Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Vol. IX, Boulder, Colo., 1965), Amer.
Math. Soc., Providence, R.I., 1966, 347–351.
[67a] On the equations defining abelian varieties. II. Invent. Math. 3, 1967, 75–135.
[67b] On the equations defining abelian varieties. III. Invent. Math. 3, 1967, 215–
244.
[67c] Pathologies. III. Amer. J. Math. 89, 1967, 94–104.
[67d] Abelian quotients of the Teichmüller modular group. J. Analyse Math. 18,
1967, 227–244.
[68a] Deformations and liftings of finite, commutative group schemes (with F.
Oort). Invent. Math. 5, 1968, 317–334.
[68b] Periods of a moduli space of bundles on curves (with P. Newstead). Amer. J.
Math. 90, 1968, 1200–1208.
[69a] Enriques’ classification of surfaces in char p. I. In Global Analysis (Papers
in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, 325–339.
[69b] Bi-extensions of formal groups. In Algebraic Geometry (Internat. Colloq.,
Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, London, 1969,
307–322.
[69c] A note of Shimura’s paper ”Discontinuous groups and abelian varieties”.
Math. Ann. 181, 1969, 345–351.
[69d] Rational equivalence of 0-cycles on surfaces. J. Math. Kyoto Univ. 9, 1969,
195–204.
[69e] The irreducibility of the space of curves of a given genus (with P. Deligne).
Publ. Math. de l’I.H.É.S. No. 36, 1969, 75–109.
[70] Varieties defined by quadratic equations (with an appendix by G. Kempf).
In Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969),
Edizioni Cremonese, Rome, 1970, 29–100.
[71a] Theta characteristics of an algebraic curve. Ann. Sci. École Norm. Sup. (4)
4, 1971, 181–192.
[71b] A remark on Mahler’s compactness theorem. Proc. Amer. Math. Soc. 28,
1971, 289–294.
[71c] The structure of the moduli spaces of curves and abelian varieties. In
Actes du Congrès International des Mathématiciens (Nice, 1970), GauthierVillars, Paris, 1971, Tome 1, 457–465.
xvi
Bibliography
[72a] An analytic construction of degenerating curves over complete local rings.
Compositio Math. 24, 1972, 129–174.
[72b] An analytic construction of degenerating abelian varieties over complete
rings. Compositio Math. 24, 1972, 239–272.
[72c] Some elementary examples of unirational varieties which are not rational
(with M. Artin). Proc. London Math. Soc. (3) 25, 1972, 75–95.
[72d] Introduction to the theory of moduli (with K. Suominen). In Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math.), WoltersNoordhoff, Groningen, 1972, 171–222.
[73a] A rank 2 vector bundle on P4 with 15, 000 symmetries (with G. Horrocks).
Topology 12, 1973, 63–81.
[73b] An example of a unirational 3-fold which is not rational. In Atti del Convegno Internazionale di Geometria a Celebrazione del Contenario della
Nascita di Federigo Enriques, Accademia Nazionale dei Lincei, Rome,
1973, p. 99.
[73c] A remark on the paper of M. Schlessinger. In Complex Analysis, 1972 (Proc.
Conf., Rice Univ., Houston, Tex., 1972), Vol. I: Geometry of Singularities.
Rice Univ. Studies 59, no. 1, 1973, 113–117.
[73d] Introduction to Part I of Oscar Zariski: Collected Papers, Volume I, Foundations of Algebraic Geometry and Resolution of Singularities. The MIT Press,
Cambridge, Massachusetts and London, England, 1973, 3–6.
[73e] Introduction to Part II of Oscar Zariski: Collected Papers, Volume II, Holomorphic Functions and Linear Systems. The MIT Press, Cambridge, Massachusetts and London, England, 1973, 175–181.
[74] Prym varieties. I. In Contributions to Analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, 325–350.
[75a] A new approach to compactifying locally symmetric varieties. In Discrete
Subgroups of Lie Groups and Applications to Moduli (Internat. Colloq.,
Bombay, 1973), Oxford Univ. Press, Bombay, 1975, 211–224.
[75b] Matsusaka’s big theorem (with D. Lieberman). In Algebraic Geometry (Proc.
Sympos. Pure Math., Vol. XXIX, Humboldt State Univ., Arcata, Calif.,
1974), Amer. Math. Soc., Providence, R.I., 1975, 513–530.
[75c] The self-intersection formula and the “formule-clef” (with A.T. Lascu and
D.B. Scott). Math. Proc. Cambridge Philos. Soc. 78, 1975, 117–123.
[75d] Pathologies IV. Amer. J. Math. 97, no. 3, 1975, 847–849.
[76a] Hilbert’s fourteenth problem—the finite generation of subrings such as rings
of invariants. In Mathematical Developments Arising from Hilbert Problems
(Proc. Sympos. Pure Math., Vol. XXVIII, Northern Illinois Univ., De Kalb,
Ill., 1974), Amer. Math. Soc., Providence, R.I., 1976, 431–444.
[76b] The projectivity of the moduli space of stable curves. I: Preliminaries on
“det” and “Div” (with F.F. Knudsen). Math. Scand. 39, no. 1, 1976, 19–55.
[76c] Enriques’ classification of surfaces in char. p. III (with E. Bombieri). Invent.
Math. 35, 1976, 197–232.
Algebraic Geometry
xvii
[77a] Enriques’ classification of surfaces in char. p. II (with E. Bombieri). In Complex Analysis and Algebraic Geometry, Iwanami Shoten, Tokyo, 1977, 23–
42.
[77b] Stability of projective varieties. Lectures given at the “Institut des Hautes
Études Scientifiques”, Bures-sur-Yvette, March-April 1976. Monographie
de l’Enseignement Mathématique, No. 24. L’Enseignement Mathématique
23, 1977, 39–110.
[77c] Hirzebruch’s proportionality theorem in the noncompact case. Invent. Math.
42, 1977, 239–272.
[78a] An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related
non-linear equations. In Proceedings of the International Symposium on
Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Book Store,
Tokyo, 1978, pp. 115–153.
[78b] The work of C.P. Ramanujam in algebraic geometry. In C.P. Ramanujam—
a Tribute, Tata Inst. Fund. Res. Studies in Math., 8, Springer-Verlag, 1978,
8–10.
[78c] Some footnotes to the work of C.P. Ramanujam. ibid., 247–262.
[78d] Fields medals. IV. An instinct for the key idea (with J. Tate). Science 202,
no. 4369, 1978, 737–739.
[79a] An algebraic surface with K ample, (K 2 ) = 9, pg = q = 0. Amer. J. Math.
101, no. 1, 1979, 233–244.
[79b] The spectrum of difference operators and algebraic curves (with P. van Moerbeke). Acta Math. 143, no. 1–2, 1979, 93–154.
[81] Singularities from the point of view of global moduli problems (abstract). In
Leopoldina-Symposion: Singularitäten—Singularities [Leopoldina Symposium: Singularities] held in Thüringen, May 3–7, 1978. Nova Acta Leopoldina, n.F., Bd. 52, nr. 240, Johann Ambrosius Barth, Leipzig, 1981, p. 161.
[82] On the Kodaira dimension of the moduli space of curves (with J. Harris, with
an appendix by W. Fulton). Invent. Math. 67, no. 1, 1982, 23–88.
[83a] On the Kodaira dimension of the Siegel modular variety. In Algebraic
Geometry—Open Problems (Ravello, 1982), Lecture Notes in Math., 997,
Springer-Verlag, 1983, 348–375,
[83b] Towards an enumerative geometry of the moduli space of curves. In Arithmetic and Geometry Vol. II, Progr. Math., 36, Birkhäuser Boston, Boston,
Mass, 1983, 271–328.
[84a] Proof of the convexity theorem. An appendix to a paper by Linda Ness, “A
stratification of the null cone via moment map, Amer. J. Math. 106, 1984,
pp. 1281-1329” Amer. J. Math. 106, 1984, 1326–1329.
[86] Oscar Zariski: 1899–1986. Notices Amer. Math. Soc. 33, no. 6, 1986, 891–
894.
[88] Oscar Zariski and his work. A joint AMS–MAA lecture presented in Atlanta,
Georgia, January 1988. AMS–MAA Joint Lecture Series. American Mathematical Society, Providence, R.I., 1988. 1 video cassette (NTSC; VHS) (60
min.)
xviii
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[90]
A foreword for non-mathematicians. In The Unreal Life of Oscar Zariski
by Carol Parikh, Academic Press, Inc., Boston, Mass., 1990, pp. xv–xxvii;
Springer Verlag, 2008, pp. xiii–xxii.
What can be computed in algebraic geometry? (with D. Bayer). In Computational Algebraic Geometry and Commutative Algebra (Cortona, 1991),
Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, U.K., 1993,
pp. 1–48.
In memoriam: George R. Kempf, 1944–2002. Amer. J. Math. 124, no. 6,
2002, iii–iv.
The boundary of moduli schemes. Mimeographed notes, Summer Institute
in Algebraic Geometry, Amer. Math. Soc., Woods Hole, 1964, 8 pp.
Further comments on boundary points. Mimeographed notes, Summer Institute in Algebraic Geometry, Amer. Math. Soc., Woods Hole, 1964, 7 pp.
Abstract theta functions (mimeographed notes by H. Pittie). Advanced Science Seminar in Algebraic Geometry, Sponsored by the National Science
Foundation, Bowdoin College, Summer 1967, 15 pp.
Degeneration of algebraic theta functions. Handwritten manuscript, 22 pp.
[93]
[02]
[u64a]
[u64b]
[u67a]
[u67b]
Vision
Books
1. Filtering, Segmentation and Depth (with Mark Nitzberg and T. Shiota). Lecture
Notes in Computer Science 662, Springer-Verlag, 1993.
2. Two- and Three-dimensional Patterns of the Face (with Peter Giblin, Gaile Gordon, Peter Hallinan and Alan Yuille). AK Peters, 1999.
3. Pattern Theory: The Stochastic Analysis of Real World Signals (with A. Desolneux). in final stages of preparation.
Papers
1. The Representation of Shape (with Andy Latto and Jayant Shah). In Proceedings of the 1984 IEEE Workshop on Computer Vision, 1984, pp. 183–191.
2. Boundary Detection by Minimizing Functionals I (with Jayant Shah). In Image
Understanding 1989, ed. by Shimon Ullman & Whitman Richards, Ablex Press,
1990, pp. 19–43. Preliminary version in 1985 IEEE Conference on Computer
Vision and Pattern Recognition (CVPR), 1985, pp. 22–26.
3. The Problem of Robust Shape Descriptors. In Proc. 1st IEEE Int. Conf. Comp.
Vision (ICCV), 1987, pp. 602–606.
4. Optimal Approximations of Piecewise Smooth Functions and Associated Variational Problems (with Jayant Shah). Comm. Pure Appl. Math., 1989, 42,
pp. 577–685.
Vision
xix
5. The 2.1D Sketch (with Mark Nitzberg). In Proc. 3rd IEEE Int. Conf. Comp.
Vision (ICCV), 1990, pp. 138–144.
6. Parametrizing Exemplars of Categories. J. Cognitive Neuroscience, 1991, 3,
pp. 87–88.
7. Mathematical Theories of Shape: do they model perception?. In Proc. Conference 1570, Soc. Photo-optical & Ind. Engineers, 1991, pp. 2–10.
8. Texture Segmentation by Minimizing Vector-Valued Energy Functionals: the
coupled membrane model (with Tai Sing Lee and Alan Yuille). Proc. European
Conf. Comp. Vision, 1992, Lecture Notes in Computer Science 588, SpringerVerlag, 1992, pp. 165–173.
9. A Bayesian Treatment of the Stereo Correspondence Problem Using HalfOccluded Regions (with Peter Belhumeur). Proc. IEEE Conf. Comp. Vision and
Pattern Recognition, 1992 (CVPR), pp. 506–512.
10. Elastica and Computer Vision. In Algebraic Geometry and its Applications
(West Lafayette, IN, 1990), 491–506, Springer-Verlag, 1994.
11. Commentary on Grenander & Miller “Representations of Knowledge in Complex Systems”. Proc. Royal Stat. Soc., 1994.
12. Pattern Theory: A Unifying Perspective. In First European Congress of Mathematics: Paris, July 6–10, 1992, Vol. 1. Invited lectures (Progress in mathematics, Vol. 119), Birkhäuser, 1994, pp. 187–224. Revised version in Perception
as Bayesian Inference, ed. D. Knill and W. Richards, Cambridge Univ. Press,
1996, pp. 25–62; also in Fields Medallists’ lectures, World Sci. Ser. 20th Century Math., Vol. 5, World Sci. Publ., River Edge, NJ, 1997, pp. 226–261; 2nd
edition: ibid., Vol. 9, 2003, pp. 234–269.
13. Chordal completions of planar graphs (with Fan Chung). J. of Combinatorics,
62, 1994, pp. 96–106.
14. Bayesian Rationale for the Variational Formulation. In Geometry-Driven Diffusion in Computer Vision, B.M. ter Haar Romeny editor, Kluwer Academic,
1994, pp. 135–146.
15. The Statistical Description of Visual Signals, International Congress of Industrial and Applied Math. 1995 ed. K. Kirshgassner, O. Mahrenholtz & R. Mennicken, Akademie Verlag, 1996.
16. Review of Variational Methods in image segmentation by J-M Morel & S. Solimini. Bull. Amer. Math. Soc., 33, 1996, pp. 211–216.
17. Learning Generic Prior Models for Visual Computation (with Song Chun Zhu).
In Proc. Conf. Comp. Vision and Pattern Rec., Comp Sci Press, 1997, 463–469
18. FRAME: Filters, Random Fields and Maximum Entropy (with Song Chun Zhu
and Yingnian Wu). Int. J. Comp. Vis., 27, 1998, pp. 107–126.
19. Minimax Entropy Principle and Its Application to Texture Modeling (with
Song Chun Zhu and Yingnian Wu). Neural Computation, 9, 1997, pp. 1627–
60.
20. GRADE: Gibbs Reaction and Diffusion Equations (with Song Chun Zhu). In
Proc. 6th Int. Conf. Comp. Vision, IEEE Computer Society, 1998, pp. 847–854.
21. Prior Learning and Gibbs Reaction-Diffusion (with Song Chun Zhu). IEEE
Trans. Patt. Anal. and Mach. Int., 19, 1997, pp. 1236–50.
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Conf. Comp. Vision and Pattern Rec., Comp Sci Press, 2000, pp. 324–331.
24. Stochastic Models for Generic Images (with Basilis Gidas). Quarterly Appl.
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25. Occlusion models for natural images: A statistical study of a scale-invariant
dead-leaves model (with Ann Lee and Jinggang Huang). Int. J. Computer Vision, 41, 2001, pp. 35–59.
26. Surface evolution under curvature flow (with Conglin Lu and Yan Cao). Special
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27. Geometric Structure Estimation of Axially Symmetric Pots from Small Fragments (with Yan Cao). In Proc. of Int. Conf. on Signal Processing, Pattern
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the European Math. Society, 8, 2006, pp. 1–48.
31. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
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36. A Stochastic Grammar of Images (with Song Chun Zhu). Foundations and
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