Totally geodesic subvarieties of the moduli space of curves and linear systems

2023/10/09 by Benirschke, Frederik
#Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.05345

Abstract

We construct a linear system on a general curve in a totally geodesic subvariety of the moduli space of curves. As a consequence, we obtain rank bounds for totally geodesic subvarieties of dimension at least two. Furthermore, we classify totally geodesic subvarieties of dimension at least two in strata with at most two zeros.

Related

• Totally geodesic submanifolds of Teichmuller space
• The boundary of a totally geodesic subvariety of moduli space
• Totally geodesic subvarieties in the moduli space of curves
• The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces
• Bounded geodesics in moduli space