Cohomology on Toric Varieties and Local Cohomology with Monomial Supports

@article{Eisenbud2000CohomologyOT,
  title={Cohomology on Toric Varieties and Local Cohomology with Monomial Supports},
  author={David Eisenbud and Mircea Mustala and Michael Stillman},
  journal={J. Symb. Comput.},
  year={2000},
  volume={29},
  pages={583-600}
}
In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The ith local cohomology of an S-module P with supports in an ideal B is the limit HB(P ) = lim −→ ` Ext(S/B`, P ), 
Highly Cited
This paper has 39 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-6 of 6 references

Local cohomology at monomial ideals

  • M. 73–93. Mustaţǎ
  • J. Symb. Comput.,
  • 2000
Highly Influential
4 Excerpts

In Introduction to Toric Varieties, volume

  • W. Springer. Fulton
  • Annals of Mathematical Studies,
  • 1993
2 Excerpts

Lyubeznik : On the vanishing of local cohomology modules

  • G. C. Huneke
  • Invent . Math .
  • 1967

Macaulay 2: a system for computation in algebraic geometry and

  • NJ Princeton
  • Topologie Algebrique et Theorie des Faisceax,
  • 1958

Similar Papers

Loading similar papers…