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arXiv · 2105.01483

On the degree of curves with prescribed multiplicities and bounded negativity

Carlos Galindo·Francisco Monserrat·Carlos-Jesús Moreno-Ávila·Elvira Pérez-Callejo
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Abstract

We provide a lower bound on the degree of curves of the projective plane $\mathbb{P}^2$ passing through the centers of a divisorial valuation $\nu$ of $\mathbb{P}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type constant of $\nu$, $\hat{\mu}(\nu)$, constant that is crucial in the Nagata-type valuative conjecture. We also give some results related to the bounded negativity conjecture concerning those rational surfaces having the projective plane as a relatively minimal model.

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Carlos Galindo, Francisco Monserrat, Carlos-Jesús Moreno-Ávila, Elvira Pérez-Callejo. 2021-05-04. On the degree of curves with prescribed multiplicities and bounded negativity. https://doi.org/10.1093/imrn%2Frnac085

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