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

Pavlov, Alexander

doi:10.1090/proc/14782

Koszul duality between Betti and Cohomology numbers in the Calabi-Yau case
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Proc. Amer. Math. Soc. 148 (2020), 1373-1381 Request permission

Abstract:

Let $X$ be a smooth projective Calabi-Yau variety and let $L$ be 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 numbers. This similarity is realized via the box-product resolution of the diagonal $\Delta _X \subset X \times X$.

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