Algebraic Geometry Seminar

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Connectedness of the moduli space of Artin-Schreier curves

Speaker: Huy Dang, University of Virginia

Location: Warren Weaver Hall 317

Date: Tuesday, December 4, 2018, 3:30 p.m.

Synopsis:

In this talk, the connectedness of the moduli space of Artin-Schreier curves with fixed genus over an algebraically closed field will be discussed. Pries and Zhu introduce a combinatorial description that partitions the moduli space into irreducible strata and tells us partially how they fit together within the moduli space. We continue their work of studying the relations between the geometry of the strata and their combinatorial data. As an application, when the characteristic is equal to 3, the moduli space is connected for every possible genus. When the characteristic is greater than 3, we show that the moduli space is connected when the genus is sufficiently large, and the bound depends on the characteristic.