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Article

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

Proceedings of the American Mathematical Society. 2020. Vol. 148. No. 4. P. 1373-1381.

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 ΔX ⊂ X × X.