Hilbert-Mumford criterion for nodal curves

Abstract

We prove by 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 Hasset on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solved a question raised by Mumford and Gieseker to prove the Chow asymptotic stability of stable nodal curves by Hilbert-Mumford criterion.

References in corpus (4)

• CM Stability and the Generalized Futaki Invariant I
• Nonexistence of asymptotic GIT compactification
• A geometric invariant theory construction of moduli spaces of stable maps
• GIT Constructions of Moduli Spaces of Stable Curves and Maps

Cited by in corpus (6)

• Compactifications of the universal Jacobian over curves with marked points
• Projective embedding of log Riemann surfaces and K-stability
• On GIT quotients of Hilbert and Chow schemes of curves
• Asymptotic Chow stability of toric Del Pezzo surfaces
• A decomposition formula for J-stability and its applications
• Fubini-Study forms on punctured Riemann surfaces