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 Eugene Stillman},
  journal={J. Symb. Comput.},
  year={2000},
  volume={29},
  pages={583-600}
}
We 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… 
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