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)

Abstract

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
• Refereed: Yes
• 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: 1058-6458
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300490		Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations	Michael Wemyss	Engineering and Physical Sciences Research Council (EPSRC)	WT5128463 EP/R034826/1	M&S - Mathematics