Hodge numbers are not derived invariants in positive characteristic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2021
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| _version_ | 1866908231988674560 |
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| author | Addington, Nicolas Bragg, Daniel |
| author_facet | Addington, Nicolas Bragg, Daniel |
| contents | We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply connected while pi_1(M) = (Z/3)^2. In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0.
In an appendix, we give a streamlined proof of Abuaf's result that the ring H^*(O) is a derived invariant of complex threefolds and fourfolds.
A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that h^{0,3} is not a derived invariant in any positive characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_09949 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hodge numbers are not derived invariants in positive characteristic Addington, Nicolas Bragg, Daniel Algebraic Geometry Number Theory We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply connected while pi_1(M) = (Z/3)^2. In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0. In an appendix, we give a streamlined proof of Abuaf's result that the ring H^*(O) is a derived invariant of complex threefolds and fourfolds. A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that h^{0,3} is not a derived invariant in any positive characteristic. |
| title | Hodge numbers are not derived invariants in positive characteristic |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2106.09949 |