BPS invariants from $p$-adic integrals
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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_ | 1866910323849560064 |
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| author | Carocci, Francesca Orecchia, Giulio Wyss, Dimitri |
| author_facet | Carocci, Francesca Orecchia, Giulio Wyss, Dimitri |
| contents | We define $p$-adic BPS or $p$BPS-invariants for moduli spaces $M_{β,χ}$ of 1-dimensional sheaves on del Pezzo surfaces by means of integration over a non-archimedean local field $F$ . Our definition relies on a canonical measure $μ_{can}$ on the $F$-analytic manifold associated to $M_{β,χ}$ and the $p$BPS-invariants are integrals of natural $\mathbb{G}_m$-gerbes with respect to $μ_{can}$. A similar construction can be done for meromorphic Higgs bundles on a curve.
Our main theorem is a $χ$-independence result for these $p$BPS-invariants. For 1-dimensional sheaves on del Pezzo surfaces and meromorphic Higgs bundles, we obtain as a corollary the agreement of $p$BPS with usual BPS-invariants trough a result of Maulik-Shen. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_12103 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | BPS invariants from $p$-adic integrals Carocci, Francesca Orecchia, Giulio Wyss, Dimitri Algebraic Geometry We define $p$-adic BPS or $p$BPS-invariants for moduli spaces $M_{β,χ}$ of 1-dimensional sheaves on del Pezzo surfaces by means of integration over a non-archimedean local field $F$ . Our definition relies on a canonical measure $μ_{can}$ on the $F$-analytic manifold associated to $M_{β,χ}$ and the $p$BPS-invariants are integrals of natural $\mathbb{G}_m$-gerbes with respect to $μ_{can}$. A similar construction can be done for meromorphic Higgs bundles on a curve. Our main theorem is a $χ$-independence result for these $p$BPS-invariants. For 1-dimensional sheaves on del Pezzo surfaces and meromorphic Higgs bundles, we obtain as a corollary the agreement of $p$BPS with usual BPS-invariants trough a result of Maulik-Shen. |
| title | BPS invariants from $p$-adic integrals |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2112.12103 |