Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913580588204032 |
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| author | Zhao, Junyan |
| author_facet | Zhao, Junyan |
| contents | In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for $d=2,3,4$, these K-moduli of pairs are isomorphic to the K-moduli spaces of del Pezzo surfaces. For $d=1$, we prove that they are different by exhibiting some walls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12339 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability Zhao, Junyan Algebraic Geometry In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for $d=2,3,4$, these K-moduli of pairs are isomorphic to the K-moduli spaces of del Pezzo surfaces. For $d=1$, we prove that they are different by exhibiting some walls. |
| title | Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2301.12339 |