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Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme

Gregory G. Smith
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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.

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Gregory G. Smith. 1998-07-29. Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme. https://doi.org/10.1006/jsco.1999.0399

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