Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections
| Autor: | Lopez, Angelo Felice, Raychaudhury, Debaditya |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We characterize the existence of an Ulrich vector bundle on a variety $X \subset P^N$ in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension $n \ge 4$, which if $n=4$ is very general and not of type $(2,2)$, does not carry any Ulrich bundles of rank $r \le 3$ unless $n=4, r=2$ and $X$ is a quadric. Comment: v2: added link to a file with the Mathematica codes used to perform the calculations; v3: slightly improved statement and proof of Cor.1 (now sharp), updated some reference; v4: replaced a reference used in the proof of Thm. 1 |
| Databáze: | arXiv |
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