Moduli of surfaces fibered in log Calabi-Yau pairs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911159729258496 |
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| author | Inchiostro, Giovanni Svaldi, Roberto Zhao, Junyan |
| author_facet | Inchiostro, Giovanni Svaldi, Roberto Zhao, Junyan |
| contents | We study the moduli spaces of surface pairs $(X,D)$ admitting a log Calabi--Yau fibration $(X,D) \to C$. We develop a series of results on stable reduction and apply them to give an explicit description of the boundary of the KSBA compactification. Three interesting cases where our results apply are: (1) divisors on $\mathbb{P}^1 \times \mathbb{P}^1$ of bidegree $(2n,m)$; (2) K3 surfaces which map $2:1$ to $\mathbb{F}_n$, with $X=\mathbb{F}_n$ and $D$ the ramification locus, or (3) elliptic surfaces with either a section or a bisection.
The main tools employed are stable quasimaps, the canonical bundle formula, and the minimal model program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli of surfaces fibered in log Calabi-Yau pairs Inchiostro, Giovanni Svaldi, Roberto Zhao, Junyan Algebraic Geometry We study the moduli spaces of surface pairs $(X,D)$ admitting a log Calabi--Yau fibration $(X,D) \to C$. We develop a series of results on stable reduction and apply them to give an explicit description of the boundary of the KSBA compactification. Three interesting cases where our results apply are: (1) divisors on $\mathbb{P}^1 \times \mathbb{P}^1$ of bidegree $(2n,m)$; (2) K3 surfaces which map $2:1$ to $\mathbb{F}_n$, with $X=\mathbb{F}_n$ and $D$ the ramification locus, or (3) elliptic surfaces with either a section or a bisection. The main tools employed are stable quasimaps, the canonical bundle formula, and the minimal model program. |
| title | Moduli of surfaces fibered in log Calabi-Yau pairs |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.14145 |