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arXiv · 1908.00049

Automorphisms of unnodal Enriques surfaces

Gebhard Martin
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Abstract

It follows from an observation of A. Coble in 1919 that the automorphism group of an unnodal Enriques surface contains the $2$-congruence subgroup of the Weyl group of the $E_{10}$-lattice. In this article, we determine how much bigger the automorphism group of an unnodal Enriques surface can be. Furthermore, we show that the automorphism group is in fact equal to the $2$-congruence subgroup for generic Enriques surfaces in arbitrary characteristic (under the additional assumption that the Enriques surface is ordinary if the characteristic is $2$), improving the corresponding result of W. Barth and C. Peters for very general Enriques surfaces over the complex numbers.

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Gebhard Martin. 2019-07-31. Automorphisms of unnodal Enriques surfaces. https://arxiv.org/abs/1908.00049

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