Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme

Abstract

Let X be a projective scheme; let M and N be two coherent O_X-modules. Given an integer m, we present an algorithm for computing the global extension module Ext^m(X;M,N). In particular, this allows one to compute the sheaf cohomology H^m(X,N) and to construct the sheaf corresponding to an element of the module Ext^1(X;M,N). This algorithm can be implemented using only the computation of Grobner bases ans syzygies, and it has been implemented in the computer algebra system Macaulay2.

18 pages. amsLaTeX. no figures. Also available at http://math.berkeley.edu/~ggsmith

References in corpus (1)

• What can be computed in algebraic geometry?

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