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arXiv · 2101.07187

On the Bounded Negativity Conjecture and singular plane curves

Alexandru Dimca·Brian Harbourne·Gabriel Sticlaru
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Abstract

There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free conjectures as a replacement. We also develop bounds on numerical characteristics of curves constraining their negativity. For example, we show that the $H$-constant of a rational curve $C$ with at most $9$ singular points satisfies $H(C)>-2$ regardless of the characteristic.

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Alexandru Dimca, Brian Harbourne, Gabriel Sticlaru. 2021-01-18. On the Bounded Negativity Conjecture and singular plane curves. https://arxiv.org/abs/2101.07187

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