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arXiv · 1905.03531

Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces

Carlos Galindo·Francisco Monserrat·Carlos-Jesús Moreno-Ávila
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Abstract

We consider flags $E_\bullet=\{X\supset E\supset \{q\}\}$, where $E$ is an exceptional divisor defining a non-positive at infinity divisorial valuation $\nu_E$ of a Hirzebruch surface $\mathbb{F}_\delta$ and $X$ the surface given by $\nu_E,$ and determine an analogue of the Seshadri constant for pairs $(\nu_E,D)$, $D$ being a big divisor on $\mathbb{F}_\delta$. The main result is an explicit computation of the vertices of the Newton-Okounkov bodies of pairs $(E_\bullet,D)$ as above, showing that they are quadrilaterals or triangles and distinguishing one case from another.

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Carlos Galindo, Francisco Monserrat, Carlos-Jesús Moreno-Ávila. 2019-05-09. Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces. https://doi.org/10.2989/16073606.2022.2146020

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