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arXiv · 2602.15703

Nef divisors of surfaces given by pencils at infinity

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

We give generators for the nef cone and the cone of curves of rational surfaces obtained by blowing-up the complex projective plane at a set of points $\mathcal{B} \cup \mathcal{D}$, where $\mathcal{B}$ is the set of (proper and infinitely near) base points of a pencil associated with a curve having one place at infinity, and $\mathcal{D}$ is a set of finitely many infinitely near free points on the strict transforms of curves of the pencil. We also prove that, when the pencil is given by an AMS-type curve and $\mathcal{D}$ contains at most two free points on any curve considered, the Cox ring of the obtained surface is finitely generated.

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Carlos Galindo, Francisco Monserrat, Carlos-Jesús Moreno-Ávila, Elvira Pérez-Callejo. 2026-02-17. Nef divisors of surfaces given by pencils at infinity. https://arxiv.org/abs/2602.15703

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