Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme

Details Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme

1998-07-29

arxiv.org/abs/math/9807170v1

Journal of Symbolic Computation 29 (2000) 729-746

Mathematics

Algebraic Geometry

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

Scientific paper

10.1006/jsco.1999.0399

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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