Counting surfaces on Calabi-Yau 4-folds I: Foundations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918022326779904 |
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| author | Bae, Younghan Kool, Martijn Park, Hyeonjun |
| author_facet | Bae, Younghan Kool, Martijn Park, Hyeonjun |
| contents | This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce \emph{two} types of moduli spaces of stable pairs. We show that all three moduli spaces are related by GIT wall-crossing and parametrize stable objects in the bounded derived category.
We construct \emph{reduced} Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci. As an application, we show that the variational Hodge conjecture holds for any family of Calabi-Yau 4-folds supporting a non-zero reduced virtual cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09474 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Counting surfaces on Calabi-Yau 4-folds I: Foundations Bae, Younghan Kool, Martijn Park, Hyeonjun Algebraic Geometry High Energy Physics - Theory 14N35 (Primary) 14D07, 14F08, 14J35, 14J60, 14L24 (Secondary) This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce \emph{two} types of moduli spaces of stable pairs. We show that all three moduli spaces are related by GIT wall-crossing and parametrize stable objects in the bounded derived category. We construct \emph{reduced} Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci. As an application, we show that the variational Hodge conjecture holds for any family of Calabi-Yau 4-folds supporting a non-zero reduced virtual cycle. |
| title | Counting surfaces on Calabi-Yau 4-folds I: Foundations |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35 (Primary) 14D07, 14F08, 14J35, 14J60, 14L24 (Secondary) |
| url | https://arxiv.org/abs/2208.09474 |