Extremal divisors on moduli spaces of K3 surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912753744084992 |
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| author | Barros, Ignacio Flapan, Laure Zuffetti, Riccardo |
| author_facet | Barros, Ignacio Flapan, Laure Zuffetti, Riccardo |
| contents | We establish criteria for when Noether--Lefschetz divisors generate an extremal ray in the cone of pseudoeffective divisors of an orthogonal modular variety. In particular, we exhibit many extremal rays of the cone of pseudoeffective divisors on any moduli space~$\mathcal{F}_{2d}$ of quasi-polarized K3 surfaces of degree $d$, as well as on any normal projective $\mathbb{Q}$-factorial compactification $\overline{\mathcal{F}}_{2d}$ of $\mathcal{F}_{2d}$ lying over the Baily--Borel compactification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16730 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal divisors on moduli spaces of K3 surfaces Barros, Ignacio Flapan, Laure Zuffetti, Riccardo Algebraic Geometry Number Theory We establish criteria for when Noether--Lefschetz divisors generate an extremal ray in the cone of pseudoeffective divisors of an orthogonal modular variety. In particular, we exhibit many extremal rays of the cone of pseudoeffective divisors on any moduli space~$\mathcal{F}_{2d}$ of quasi-polarized K3 surfaces of degree $d$, as well as on any normal projective $\mathbb{Q}$-factorial compactification $\overline{\mathcal{F}}_{2d}$ of $\mathcal{F}_{2d}$ lying over the Baily--Borel compactification. |
| title | Extremal divisors on moduli spaces of K3 surfaces |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2504.16730 |