One-dimensional substacks of the moduli stack of Deligne-Mumford stable curves

arXivmath/0612802MaRDI QIDQ6478517

Jörg Zintl

Publication date: 27 December 2006

Abstract: There is a well-known stratification of the moduli space $M_g$ of Deligne-Mumford stable curves of genus $g$ by the loci of stable curves with a fixed number $i$ of nodes, where $ile3g-3$. The associated moduli stack ${calM}_g$ admits an analogous stratification. Our main objects of study are those one-dimensional substacks of the moduli stack, which are the irreducible components of the stratum corresponding to stable curves with exactly $3g-4$ nodes. We describe these substacks explicitely as quotient stacks, and relate them to other, and simpler, moduli stacks of (permutation classes of) pointed stable curves. In an appendix, an extensive compendium on quotient stacks is provided.

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Automorphisms of curves (14H37) Generalizations (algebraic spaces, stacks) (14A20)

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