Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929388137742336 |
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| author | Si, Fei Zhang, Feinuo |
| author_facet | Si, Fei Zhang, Feinuo |
| contents | In this paper, we study the asymptotic behaviors of the Betti numbers and Picard numbers of the moduli space $M_{β,χ}$ of one-dimensional sheaves supported in a curve class $β$ on $S$ with Euler characteristic $χ$. We determine the intersection cohomology Betti numbers of $M_{β,χ}$ when $S$ is a del Pezzo surface and $β$ is sufficiently positive. As an application, we formulate a $P = C$ conjecture regarding the refined BPS invariants for local del Pezzo surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces Si, Fei Zhang, Feinuo Algebraic Geometry In this paper, we study the asymptotic behaviors of the Betti numbers and Picard numbers of the moduli space $M_{β,χ}$ of one-dimensional sheaves supported in a curve class $β$ on $S$ with Euler characteristic $χ$. We determine the intersection cohomology Betti numbers of $M_{β,χ}$ when $S$ is a del Pezzo surface and $β$ is sufficiently positive. As an application, we formulate a $P = C$ conjecture regarding the refined BPS invariants for local del Pezzo surfaces. |
| title | Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.11512 |