Cellular Sheaf Cohomology in Polymake
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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 and tropical geometry.
MSC 2010 codes:05-04 14Fxx 14T05 52Bxx
This article and the polymake extension cellularSheaves were developed during the Combinatorial Algebraic Geometry Thematic Program at the Fields Institute. We are very grateful to the organizers and the institute for their hospitality. We thank Greg Smith, Bernd Sturmfels, and five anonymous referees for their careful attention to an earlier version of this manuscript. This research was supported by the Fields Institute, the Alexander von Humboldt foundation, as well as the priority program SPP1489 and the collaborative research centre SFB647 of the German science foundation (DFG).
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