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<p>We study the cohomology of broken toric varieties via the derived push-forward of the constant sheaf to a complex of polytopes, proving a Deligne-type decomposition theorem, degeneration of the associated Leray-Serre spectral sequence, and showing that the Leray filtration on their cohomology is equal to twice the weight filtration. Furthermore, we give an explicit formula for the Betti numbers of some broken toric varieties whose associated complex of polytopes is the <i>n</i>-skeleton of a higher dimensional polytope, encompassing some important examples.</p>

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Broken toric varieties and cell-compatible sheaves

  • 期刊论文

  • 发表日期：

    2025年4月13日

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  • Evan Sundbo

摘要

We study the cohomology of broken toric varieties via the derived push-forward of the constant sheaf to a complex of polytopes, proving a Deligne-type decomposition theorem, degeneration of the associated Leray-Serre spectral sequence, and showing that the Leray filtration on their cohomology is equal to twice the weight filtration. Furthermore, we give an explicit formula for the Betti numbers of some broken toric varieties whose associated complex of polytopes is the n-skeleton of a higher dimensional polytope, encompassing some important examples.