关于弱有界否定性猜想

arXiv - MATH - Algebraic Geometry Pub Date : 2024-08-27 DOI:arxiv-2408.15187

Snehajit Misra, Nabanita Ray

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引用次数: 0

摘要

在本文的第一部分，我们给出了在反烛光除数$-K_X$有效的曲面$X$的炸裂$Bl_nX$上积分曲线$C$的自交$C^2$的边界。在最后一部分中，我们证明了在曲面 $f:Y\longrightarrow B$ 的一个族中积分曲线 $C$ 的自交 $C^2$ 的弱界否定性，其中 $B$ 是一条光滑曲线。

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On Weak bounded negativity conjecture

In the first part of this article, we give bounds on self-intersections $C^2$ of integral curves $C$ on blow-ups $Bl_nX$ of surfaces $X$ with the anti-cannonical divisor $-K_X$ effective. In the last part, we prove the weak bounded negativity for self-intersections $C^2$ of integral curves $C$ in a family of surfaces $f:Y\longrightarrow B$ where $B$ is a smooth curve.

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arXiv - MATH - Algebraic Geometry

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