Seshadri constants on hyperelliptic surfaces

Hanumanthu, Krishna; Roy, Praveen Kumar

doi:10.1090/proc/14114

Seshadri constants on hyperelliptic surfaces
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by Krishna Hanumanthu and Praveen Kumar Roy PDF

Proc. Amer. Math. Soc. 146 (2018), 4175-4187 Request permission

Abstract:

We prove new results on single point Seshadri constants for ample line bundles on hyperelliptic surfaces, motivated by the results of Farnik [Arch. Math. 107 (2016), pp. 227–237]. Given a hyperelliptic surface $X$ and an ample line bundle $L$ on $X$, we show that the least Seshadri constant $\varepsilon (L)$ of $L$ is a rational number when $X$ is not of type 6. We also prove new lower bounds for the Seshadri constant $\varepsilon (L,1)$ of $L$ at a very general point.

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