Betti numbers of MCM modules over the cone of an elliptic normal curve (Q1734225)
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| English | Betti numbers of MCM modules over the cone of an elliptic normal curve |
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Betti numbers of MCM modules over the cone of an elliptic normal curve (English)
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22 March 2019
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In [\textit{ A. Pavlov}, ``Betti tables of maximal Cohen-Macaulay modules over the cone of a plane cubic'', Preprint, \url{arXiv:1511.05089}] the author obtained formulas for the Betti numbers of maximal Cohen-Macaulay modules over the cone of a smooth plane cubic. In the present paper he extends his results to normal elliptic curves in $\mathbb{P}^n$, with $n>2$. He uses Orlov's equivalence of triangulated categories. See [\textit{D. Orlov}, Prog. Math. 270, 503--531 (2009; Zbl 1200.18007)]. and derives recurrence relations for the Betti numbers. Furthermore, he applies his methods to the special cases $n = 1, 2$ and derives formulas for the Betti numbers and the numerical invariants of maximal Cohen-Macaulay modules. For background see [\textit{J. Herzog} and \textit{M. Kühl}, Adv. Stud. Pure Math. 11, 65--92 (1987; Zbl 0641.13014)].
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elliptic curves
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maximal Cohen-Macaulay modules
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Ulrich modules
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Koszul modules
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