Computing Cohomology on Toric Varieties

@article{Jurke2011ComputingCO,
  title={Computing Cohomology on Toric Varieties},
  author={Benjamin Jurke},
  journal={arXiv: Algebraic Geometry},
  year={2011}
}
  • Benjamin Jurke
  • Published 7 September 2011
  • Mathematics
  • arXiv: Algebraic Geometry
In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on the structure of the Stanley-Reisner ideal generators. A particular focus is placed on the (simplicial) Alexander duality that provides a central tool for the two known proofs of the algorithm. 
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