Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme
Algebraic Geometry
2010-03-15 v1 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.math/9807170,
title = {Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme},
author = {Gregory G. Smith},
journal= {arXiv preprint arXiv:math/9807170},
year = {2010}
}
Comments
18 pages. amsLaTeX. no figures. Also available at http://math.berkeley.edu/~ggsmith