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Cellular sheaf cohomology in Polymake

This chapter provides a guide to our 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 summarise 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 and tropical geometry.

preprint2016arXivOpen access
Lars KastnerKristin ShawAnna-Lena Winz
math.AG
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Lars KastnerKristin ShawAnna-Lena Winz

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