Moduli of elliptic surfaces of Kodaira dimension one fibered over rational curves
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911304801845248 |
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| author | Bejleri, Dori Foster, Josiah Herrero, Andres Fernandez Inchiostro, Giovanni Makarova, Svetlana Zhao, Junyan |
| author_facet | Bejleri, Dori Foster, Josiah Herrero, Andres Fernandez Inchiostro, Giovanni Makarova, Svetlana Zhao, Junyan |
| contents | In this article, we construct an infinite sequence of irreducible components of Kollár--Shepherd-Barron (KSB-) moduli spaces of surfaces of arbitrarily large volumes, and describe the boundary of each component completely. Moreover, we describe the stable reduction steps in finding the KSB-limits in an explicit combinatorial way. Our main approach is to study the moduli spaces of elliptic surfaces with Kodaira dimension one, fibered over rational curves, using the techniques of wall-crossing for KSBA moduli and twisted stable maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moduli of elliptic surfaces of Kodaira dimension one fibered over rational curves Bejleri, Dori Foster, Josiah Herrero, Andres Fernandez Inchiostro, Giovanni Makarova, Svetlana Zhao, Junyan Algebraic Geometry In this article, we construct an infinite sequence of irreducible components of Kollár--Shepherd-Barron (KSB-) moduli spaces of surfaces of arbitrarily large volumes, and describe the boundary of each component completely. Moreover, we describe the stable reduction steps in finding the KSB-limits in an explicit combinatorial way. Our main approach is to study the moduli spaces of elliptic surfaces with Kodaira dimension one, fibered over rational curves, using the techniques of wall-crossing for KSBA moduli and twisted stable maps. |
| title | Moduli of elliptic surfaces of Kodaira dimension one fibered over rational curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.05539 |