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Actions of μp on canonically polarized surfaces in characteristic p > 0

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Abstract

This paper studies the existence of non trivial \(\mu _p\) actions on a canonically polarized surface X defined over an algebraically closed field of characteristic \(p>0\). In particular, an explicit function \(f(K_X^2)\) is obtained such that if \(p>f(K_X^2)\), then there does not exist a non trivial \(\mu _p\)-action on X. This implies that the connected component of \({\mathrm {Aut}}(X)\) containing the identity is either smooth or is obtained by successive extensions by \(\alpha _p\).

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  1. Department of Mathematics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    Nikolaos Tziolas

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Part of this paper was partially written during the author’s stay at the Max Planck Institute for Mathematics in Bonn, from February 1 2019 to July 31 2019.

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Tziolas, N. Actions of μp on canonically polarized surfaces in characteristic p > 0. manuscripta math. 171, 103–153 (2023). https://doi.org/10.1007/s00229-022-01374-2

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