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 OX-modules. Given an integer m, we present an algorithm for computing the global extension module Extm(X;M,N). In particular, this allows one to compute the sheaf cohomology Hm(X,N) and to construct the sheaf corresponding to an element of the module Ext1(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.
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