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

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- by Alexander Pavlov PDF
- 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 $\Delta _X \subset X \times X$.## References

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## Additional Information

**Alexander Pavlov**- Affiliation: Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva Street, 119048 Moscow, Russia
- MR Author ID: 1309386
- Email: abpavlov@hse.ru
- Received by editor(s): October 3, 2018
- Received by editor(s) in revised form: February 23, 2019
- Published electronically: January 13, 2020
- Communicated by: Rachel Pries
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 1373-1381 - MSC (2010): Primary 13D02; Secondary 14F05, 14J32
- DOI: https://doi.org/10.1090/proc/14782
- MathSciNet review: 4069177