On the Kodaira dimension of the moduli space of hyperelliptic curves with marked points

2020/02/09 by Schwarz, Irene
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.03417

Abstract

It is known that the moduli space H_g,n of genus g stable hyperelliptic curves with n marked points is uniruled for n ≤ 4g+5. In this paper we consider the complementary case. We calculate the canonical divisor of H_g,n and show that it is effective for n=4g+6 and big for n≤ 4g+7. This leads us to conjecture that H_g,n has non-negative Kodaira dimension for n = 4g+6 and is of general type for n ≥ 4g+7.

Related

• The Kodaira dimension of moduli spaces of curves with marked points, II
• The Kodaira classification of the moduli of hyperelliptic curves
• Compactifying moduli of hyperelliptic curves
• The Geometry of the Moduli Space of Curves of Genus 23
• The Kodaira dimensions of M₂₂ and M₂₃