1089-14-322 Hirotachi Abo, David Eklund and Chris Peterson* (peterson@math.colostate.edu). Eigenschemes and deformations in the tangent bundle. An eigenscheme is a scheme that encodes information about the generalized eigenspaces of a matrix. Eigenschemes can be realized as zero-loci of sections of the tangent bundle to projective space. This talk will discuss eigenschemes, their construction via the tangent bundle, and applications of such a construction. (Received February 18, 2013) 1