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arXiv · 2202.08074

Seshadri Constants Over Fields Of Characteristic Zero

Shripad M. Garge·Arghya Pramanik
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Abstract

Let $X$ be a smooth projective variety defined over a field $k$ of characteristic $0$ and let $\mathcal{L}$ be a nef line bundle defined over $k$. We prove that if $x\in X$ is a $k$-rational point then the Seshadri constant $\epsilon(X, \mathcal{L}, x)$ over $\overline{k}$ is the same as that over $k$. We show, by constructing families of examples, that there are varieties whose global Seshadri constant $\epsilon(X)$ is zero. We also prove a result on the existence of a Seshadri curve with a natural (and necessary) hypothesis.

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Shripad M. Garge, Arghya Pramanik. 2022-02-16. Seshadri Constants Over Fields Of Characteristic Zero. https://arxiv.org/abs/2202.08074

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