Moduli spaces of weighted pointed stable curves

2002/05/01 by Brendan Hassett, Hassett, Brendan · 10 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0205009

To appear in Advances in Mathematics

arxiv created 2002/05/01 · arxiv updated 2009/11/30

Abstract

A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum of the corresponding weights is no greater than one. We construct moduli spaces for these objects using methods of the log minimal model program, and describe the induced birational morphisms between moduli spaces as the weights are varied. In the genus zero case, we explain the connection to Geometric Invariant Theory quotients of points in the projective line, and to compactifications of moduli spaces studied by Kapranov, Keel, and Losev-Manin.

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• Approximate Fiber Products of Schemes and Their Étale Homotopical Invariants
• On multiscale aspects of Kähler-Einstein metrics and algebraic geometry
• Twisted stable maps with colliding points
• Remarks on two problems by Hassett
• Smooth manifolds in G_n,2 and ℂ P^N defined by symplectic reductions of Tⁿ-action
• Moduli Theory of the r-Braid Arrangement

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• Log canonical models for the moduli space of pointed stable rational curves
• Mori's program for the moduli space of pointed stable rational curves
• Chow groups of the moduli spaces of weighted pointed stable curves of genus zero
• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• On the rationality of moduli spaces of pointed curves