π₁ of trigonal loci of strata of abelian differentials

2025/10/07 by Lönne, Michael
#14D05 primary (14F35 #14J27 secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2510.06364

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 \mathbf P\mathcal H^ev₄(6), the projectivisation of the space \mathcal H^ev₄(6) 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 E₈ by its maximal central subgroup.

Citations

• About the even minimal stratum of translation surfaces in genus 4
• Framed mapping class groups and the monodromy of strata of Abelian differentials
• Secondary Braid Groups
• On a discriminant knot group problem of Brieskorn
• Affine Artin groups and the fundamental groups of some moduli spaces

Related

• Fundamental groups of strata of abelian differentials of low codimension
• Connected components of strata of Abelian differentials over\n Teichm "uller space
• Higher spin mapping class groups and strata of Abelian differentials over Teichmüller space
• Strata of abelian differentials and the Teichmueller dynamics
• The trigonal construction in the ramified case