On the rationality of moduli spaces of pointed curves

2005/04/12 by Gianfranco Casnati, Casnati, Gianfranco, Claudio Fontanari +1 · 1 citation
Engineering · Mathematics · #14H10 #14H45 (primary) 14E08 #14L30 (secondary) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0504249

openalex publication_date 2005/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by several recent results on the geometry of the moduli spaces \Cal M_g,n of stable curves of genus g with n marked points, here we determine their birational structure for small values of g and n by exploiting suitable plane models of the general curve. More precisely, we show that \Cal M_g,n is rational for g=2 and 1≤ n≤ 12, g=3 and 1≤ n≤ 14, g=4 and 1≤ n≤ 15, g=5 and 1≤ n≤ 12.

Citations

• The unirationality of the moduli spaces of curves of genus 14 or lower
• Constructions of nontautological classes on moduli spaces of curves

Cited by

• The Kodaira classification of the moduli space of pointed curves in genus 3

Related

• On the birational geometry of moduli spaces of pointed curves
• On the rationality problem for forms of moduli spaces of stable marked\n curves of positive genus
• On the unirationality of moduli spaces of pointed curves
• Moduli spaces of weighted pointed stable curves
• Birational Geometry of moduli spaces of pointed curves