On the rationality of the moduli of higher spin curves in low genus

2013/11/01 by Pernigotti, Letizia, Verra, Alessandro
#14E05 #14E08 #14H10 #14H45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1311.0263

Abstract

The global geometry of the moduli spaces of higher spin curves and their birational classification is largely unknown for g >= 2 and r > 2. Using quite related geometric constructions, we almost complete the picture of the known results in genus g <= 4 showing the rationality of the moduli spaces of even and odd 4-spin curves of genus 3, of odd spin curves of genus 4 and of 3-spin curves of genus 4.

Related

• The moduli space of genus 4 even spin curves is rational
• The rationality of the moduli spaces of trigonal curves of odd genus
• Moduli of Curves and Spin Structures via Algebraic Geometry
• On the rational Picard group of the moduli space of higher spin curves
• The rationality of the moduli space of one-pointed ineffective spin hyperelliptic curves via an almost del Pezzo threefold