ON THE FIRST STEPS OF THE MINIMAL MODEL PROGRAM FOR THE MODULI SPACE OF STABLE POINTED CURVES. (22nd January 2023)

• Record Type: Journal Article
• Authors: Codogni, Giulio; Tasin, Luca; Viviani, Filippo
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 22:Number 1(2023)
• Page Start: 145
• Page End: 211
• Publication Date: 2023-01-22
• Subjects: Minimal model program -- moduli space of curves -- modular compactifications; 14H10 -- 14E30 -- 14D23 -- 14H20; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748021000116
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract: The aim of this paper is to study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation, and we study their geometric properties. As a particular case, we recover the first few Hassett–Keel log canonical models. As a by-product, we produce many birational morphisms from the moduli space of stable pointed curves to alternative modular projective compactifications of the moduli space of pointed curves.