On the Bounded Negativity Conjecture and singular plane curves

Alexandru Dimca; Brian Harbourne; Gabriel Sticlaru

On the Bounded Negativity Conjecture and singular plane curves

Algebraic Geometry 2021-03-23 v3

Authors: Alexandru Dimca , Brian Harbourne , Gabriel Sticlaru

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.

Keywords

rational points on curves algebraic curves singularity theory

Cite

@article{arxiv.2101.07187,
  title  = {On the Bounded Negativity Conjecture and singular plane curves},
  author = {Alexandru Dimca and Brian Harbourne and Gabriel Sticlaru},
  journal= {arXiv preprint arXiv:2101.07187},
  year   = {2021}
}

Comments

v.3. Substantially upgraded new version, having Brian Harbourne as a new co-author. All the results are now characteristic free, and there are new key examples

On the Bounded Negativity Conjecture and singular plane curves

Abstract

Keywords

Cite

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