Cohomology on Toric Varieties and Local Cohomology with Monomial Supports

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dc.creatorEisenbud, David
dc.creatorMustata, Mircea
dc.creatorStillman, Mike
dc.date2000-01-27
dc.date.accessioned2026-07-07T04:33:27Z
dc.date.available2026-07-07T04:33:27Z
dc.descriptionWe study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each component of H^i_B(R) is finite dimensional and we give an effective way to compute these components. Using Cox's description for sheaves on toric varieties, we apply these results to compute the cohomology of coherent sheaves on toric varieties. We give algorithms for this computation which have been implemented in the Macaulay 2 system. We obtain also a topological description for the cohomology of rank one torsionfree sheaves on toric varieties.
dc.description23 pages, 2 figures, uses diagrams.tex, to appear in Journal of Symbolic Computation
dc.identifierhttps://arxiv.org/abs/math/0001159
dc.identifierhttp://arxiv.org/abs/math/0001159
dc.identifierJ. Symbolic Comput. 29 (2000), no. 4-5, 583-600
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58581
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14M25 (Primary); 13D45; 14Q99 (Secondary)
dc.titleCohomology on Toric Varieties and Local Cohomology with Monomial Supports
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