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arXiv · 1711.06931

Koszul duality between Betti and Cohomology numbers in Calabi-Yau case

Alexander Pavlov
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Abstract

Let $X$ be a smooth projective Calabi-Yau variety and $L$ a Koszul line bundle on $X$. We show that for Betti numbers of a maximal Cohen-Macaulay module over the homogeneous coordinate ring $A$ of $X$ there are formulas similar to the formulas for cohomology number. This similarity is realized via the box-product resolution of the diagonal $Δ_X \subset X \times X$.

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Alexander Pavlov. 2017-11-18. Koszul duality between Betti and Cohomology numbers in Calabi-Yau case. https://arxiv.org/abs/1711.06931

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