Automorphisms of smooth canonically polarized surfaces in positive characteristic
Abstract
This paper investigates the geometry of a smooth canonically polarized surface defined over an algebraically closed field of characteristic in the case when the automorphism scheme of is not smooth. This is a situation that appears only in positive characteristic and it is closely related to the structure of the moduli stack of canonically polarized surfaces. Restrictions on certain numerical invariants of are obtained in order for Aut(X) to be smooth or not and information is provided about the structure of the component of Aut(X) containing the identity. In particular, it is shown that a smooth canonically polarized surface X with 0< K_X^2 < 3 and non smooth automorphism scheme tends to be uniruled and simply connected. Moreover, X is the purely inseparable quotient of a ruled or rational surface by a rational vector field.
Keywords
Cite
@article{arxiv.1506.08843,
title = {Automorphisms of smooth canonically polarized surfaces in positive characteristic},
author = {Nikolaos Tziolas},
journal= {arXiv preprint arXiv:1506.08843},
year = {2015}
}
Comments
This paper is a generalization to all characteristics of the paper "Automorphisms of smooth canonically polarized surfaces in characteristic 2", arXiv:1408.1291, of the same author. The results of this paper completely supersede the results of the aforementioned paper making it obsolete. 64 pages