On some modular contractions of the moduli space of stable pointed curves

Codogni, Giulio; Tasin, Luca; Viviani, Filippo

doi:10.2140/ant.2021.15.1245

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On some modular contractions of the moduli space of stable pointed curves

Giulio Codogni, Luca Tasin and Filippo Viviani

Vol. 15 (2021), No. 5, 1245–1281

DOI: 10.2140/ant.2021.15.1245

Abstract

The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves ${\bar{M}}_{g, n}$ . These new moduli spaces, which are modular compactifications of $M_{g, n}$ , are related to the minimal model program for ${\bar{M}}_{g, n}$ and have been introduced by Codogni et al. (2018). We interpret them as log canonical models of adjoint divisors and we then describe the Shokurov decomposition of a region of boundary divisors on ${\bar{M}}_{g, n}$ .

Keywords

moduli of curves, birational contractions, modular compactifications

Mathematical Subject Classification 2010

Primary: 14H10

Secondary: 14D22, 14D23, 14E30

Milestones

Received: 7 March 2020

Revised: 17 August 2020

Accepted: 9 November 2020

Published: 30 June 2021

Authors

Giulio Codogni
Dipartimento di Matematica Università degli Studi di Roma Tor Vergata Roma Italy

Luca Tasin
Dipartimento di Matematica F. Enriques Università degli Studi di Milano Milano Italy

Filippo Viviani
Dipartimento di Matematica e Fisica Università degli Studi Roma Tre Rome Italy

Vol. 15, No. 5, 2021