Cellular Sheaf Cohomology in Polymake

  title={Cellular Sheaf Cohomology in Polymake},
  author={Lars Kastner and Kristin M. Shaw and Anna-Lena Winz},
  journal={arXiv: Algebraic Geometry},
This is a guide to the polymake extension cellularSheaves. We first define cellular sheaves on polyhedral complexes in Euclidean space, as well as cosheaves, and their (co)homologies. As motivation, we summarize some results from toric and tropical geometry linking cellular sheaf cohomologies to cohomologies of algebraic varieties. We then give an overview of the structure of the extension cellularSheaves for polymake. Finally, we illustrate the usage of the extension with examples from toric… 

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ContentsIntroductionChapter I. Affine toric varieties § 1. Cones, lattices, and semigroups § 2. The definition of an affine toric variety § 3. Properties of toric varieties § 4. Differential forms on