A computational view on the non-degeneracy invariant for Enriques surfaces

Moschetti, R., Rota, F. and Schaffler, L. (2022) A computational view on the non-degeneracy invariant for Enriques surfaces. Experimental Mathematics, (doi: 10.1080/10586458.2022.2113576) (Early Online Publication)

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For an Enriques surface S, the non-degeneracy invariant nd(S) retains information on the elliptic fibrations of S and its polarizations. In the current paper, we introduce a combinatorial version of the non-degeneracy invariant which depends on S together with a configuration of smooth rational curves, and gives a lower bound for nd(S). We provide a SageMath code that computes this combinatorial invariant and we apply it in several examples. First we identify a new family of nodal Enriques surfaces satisfying nd(S)=10 which are not general and with infinite automorphism group. We obtain lower bounds on nd(S) for the Enriques surfaces with eight disjoint smooth rational curves studied by Mendes Lopes–Pardini. Finally, we recover Dolgachev and Kondō’s computation of the non-degeneracy invariant of the Enriques surfaces with finite automorphism group and provide additional information on the geometry of their elliptic fibrations.

Item Type:Articles
Status:Early Online Publication
Glasgow Author(s) Enlighten ID:Rota, Dr Franco
Authors: Moschetti, R., Rota, F., and Schaffler, L.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Experimental Mathematics
Publisher:Taylor & Francis
ISSN (Online):1944-950X
Published Online:29 August 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Experimental Mathematics 2022
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300490Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And DeformationsMichael WemyssEngineering and Physical Sciences Research Council (EPSRC)WT5128463 EP/R034826/1M&S - Mathematics