Classification of planar rational cuspidal curves. II. Log del Pezzo models
| Autor: | Palka, Karol, Pełka, Tomasz |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Proc. Lond. Math. Soc. 120 (2020), No. 5, 642-703 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/plms.12300 |
| Popis: | Let $E\subseteq \mathbb{P}^2$ be a complex curve homeomorphic to the projective line. The Negativity Conjecture asserts that the Kodaira-Iitaka dimension of $K_X+\frac{1}{2}D$, where $(X,D)\to (\mathbb{P}^{2},E)$ is a minimal log resolution, is negative. We prove structure theorems for curves satisfying this conjecture and we finish their classification up to a projective equivalence by describing the ones whose complement admits no $\mathbb{C}^{**}$-fibration. As a consequence, we show that they satisfy the Strong Rigidity Conjecture of Flenner-Zaidenberg. The proofs are based on the almost minimal model program. The obtained list contains one new series of bicuspidal curves. Comment: 50 pages |
| Databáze: | arXiv |
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