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arXiv · 1905.10197

Some Results on Seshadri constants on Surfaces of general type

Praveen Kumar Roy
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Abstract

We prove two new results for Seshadri constants on surfaces of general type. Let $X$ be a surface of general type. In the first part, inspired by \cite{B-S}, we list the possible values for the multi-point Seshadri constant $\varepsilon(K_X,x_1,x_2,...,x_r)$ when it lies between $0$ and $1/r$, where $K_X$ is the canonical line bundle on $X$. In the second part, we assume $X$ of the form $C \times C$, where $C$ is a general smooth curve of genus $g \geq 2$. Given such $X$ and an ample line bundle $L$ on $X$ with some conditions on it, we show that the global Seshadri constant of $L$ is a rational number.

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Praveen Kumar Roy. 2019-05-24. Some Results on Seshadri constants on Surfaces of general type. https://arxiv.org/abs/1905.10197

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