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Hilbert–Mumford criterion for nodal curves

Part of: Curves Complex manifolds

Published online by Cambridge University Press:  10 June 2015

Jun Li  and
Xiaowei Wang
Jun Li
Affiliation:
Stanford University, Stanford, CA 94305, USA email jli@stanford.edu
Xiaowei Wang
Affiliation:
The Chinese University of Hong Kong, Hong Kong and Rutgers University, Newark, NJ 07102, USA email xiaowwan@rutgers.edu
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Abstract

We prove by the Hilbert–Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves and of Hassett on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solves a question raised by Mumford and Gieseker, to prove the Chow asymptotic stability of stable nodal curves by the Hilbert–Mumford criterion.

Keywords

geometric invariant theoryasymptotic stabilityChow stabilityChow weightK-stabilityDonaldson–Futaki invariantmoduli of curvesone parameter subgroupsHilbert–Mumford criterion

MSC classification

Primary: 14H10: Families, moduli (algebraic)
Secondary: 32Q20: Kähler-Einstein manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 11 , November 2015 , pp. 2076 - 2130
Copyright
© The Authors 2015 

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