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arXiv · 2006.03341

Actions of $\mu_p$ on canonically polarized surfaces in characteristic p>0

Nikolaos Tziolas
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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 the automorphism scheme of X containing the identity is either smooth or is obtained by successive extensions by $\alpha_p$.

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Nikolaos Tziolas. 2020-06-05. Actions of $\mu_p$ on canonically polarized surfaces in characteristic p>0. https://arxiv.org/abs/2006.03341

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