Irreducibility of the space of cyclic covers of algebraic curves of fixed numerical type and the irreducible components of Sing (\mathfrak M_g)

2010/11/01 by Fabrizio Catanese, Catanese, Fabrizio · 1 citation
Mathematics · #14H10 #14H15 #14H30 #32G15 #32M99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1011.0316

openalex publication_date 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove irreducibility for the space of cyclic covers of fixed numerical type between smooth projective curves, and also for the space of cyclic covers of prime order and of fixed numerical-combinatorial type between moduli-stable projective curves. As an application we describe the irreducible components of the singular locus of the compactified moduli space of curves \mahfrak M_g, extending the work of Cornalba, who described the irreducible components of the singular locus of the moduli space of curves \mahfrak M_g.

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