The fundamental group of trigonal loci of strata of abelian differentials
Michael Lönne
Journal of Singularities
volume 30 (2026), 242-254
Received: 30 September 2025. In revised form: 1 March 2026
Abstract:
We investigate locally closed subspaces of projectivized strata of abelian differentials which classify trigonal curves with canonical divisor a multiple of a trigonal divisor. % We describe their orbifold structure using linear systems on Segre-Hirzebruch surfaces and obtain results for their orbifold fundamental groups.
Most notable among these orbifolds is the connected component which is the projectivisation of the space of abelian differentials on non-hyperelliptic genus 4 curves with a single zero of multiplicity 6 providing an even spin structure. Its orbifold fundamental group is identified with the quotient of the Artin group of type E_8 by its maximal central subgroup.
Author(s) information:
Michael Lönne
Mathematisches Institut der Universität Bayreuth
Universitätsstr. 30
95447 Bayreuth, Germany
email: michael.loenne@uni-bayreuth.de