K-moduli of log del Pezzo pairs and variations of GIT
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917708254150656 |
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| author | Martinez-Garcia, Jesus Papazachariou, Theodoros Stylianos Zhao, Junyan |
| author_facet | Martinez-Garcia, Jesus Papazachariou, Theodoros Stylianos Zhao, Junyan |
| contents | We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree $d$ and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, providing a natural problem in variations of K-moduli spaces. For degrees 2, 3, 4, we establish an isomorphism between the K-moduli spaces and variations of Geometric Invariant Theory compactifications, which generalizes the isomorphisms in the absolute cases established by Odaka--Spotti--Sun and Mabuchi--Mukai. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-moduli of log del Pezzo pairs and variations of GIT Martinez-Garcia, Jesus Papazachariou, Theodoros Stylianos Zhao, Junyan Algebraic Geometry We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree $d$ and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, providing a natural problem in variations of K-moduli spaces. For degrees 2, 3, 4, we establish an isomorphism between the K-moduli spaces and variations of Geometric Invariant Theory compactifications, which generalizes the isomorphisms in the absolute cases established by Odaka--Spotti--Sun and Mabuchi--Mukai. |
| title | K-moduli of log del Pezzo pairs and variations of GIT |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.20008 |