Classification of planar rational cuspidal curves II. Log del Pezzo models

Palka, Karol; Pełka, Tomasz (2020). Classification of planar rational cuspidal curves II. Log del Pezzo models. Proceedings of the London Mathematical Society, 120(5), pp. 642-703. Oxford University Press 10.1112/plms.12300

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Let E ⊆ P² be a complex curve homeomorphic to the projective line. The Negativity Conjecture asserts that the Kodaira–Iitaka dimension of K_X + 1/ 2 D , where (X, D) ⟶ (P², 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 complements admit no 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Pelka, Tomasz Ryszard

Subjects:

500 Science > 510 Mathematics

ISSN:

0024-6115

Publisher:

Oxford University Press

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

17 Feb 2020 16:17

Last Modified:

13 Sep 2020 02:30

Publisher DOI:

10.1112/plms.12300

ArXiv ID:

1810.08180

BORIS DOI:

10.7892/boris.139943

URI:

https://boris.unibe.ch/id/eprint/139943

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