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arXiv · 2305.15416

A remark on weighted Bounded Negativity for blow-ups of the projective plane

Ciro Ciliberto·Claudio Fontanari
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Abstract

Motivated by the weighted Bounded Negativity Conjecture, we prove that all but finitely many reduced and irreducible curves $C$ on the blow-up of $\mathbb{P}^2$ at $n$ points satisfy the inequality $C^2 \ge \min \{-\frac{1}{12} n (C.L +27), -2 \}$, where $L$ is the pull-back of a line. This partially improves on some result by Laface and Pokora.

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Ciro Ciliberto, Claudio Fontanari. 2023-05-10. A remark on weighted Bounded Negativity for blow-ups of the projective plane. https://arxiv.org/abs/2305.15416

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