Nonexistence of asymptotic GIT compactification

2012/12/31 by Xiaowei Wang, Chenyang Xu
Mathematics · #Algebraic Geometry and Number Theory #Compactification (mathematics) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical analysis #Mathematics #Pure mathematics #math.AG #math.DG

paper · pdf · doi:10.1215/00127094-2785806

published as Duke Math. J. 163, no. 12 (2014), 2217-2241 · Several typos are corrected according to the feedback

arxiv created 2013/01/05 · openalex publication_date 2014/09/15 · arxiv updated 2015/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We provide examples of families of (log) smooth canonically polarized varieties, including smooth weighted pointed curves and smooth hypersurfaces in P3 with large degree such that the Chow semistable limits under distinct pluricanonical embeddings do not stabilize.

Citations

• Birational Geometry of Algebraic Varieties
• Scalar Curvature and Projective Embeddings, I
• CM Stability and the Generalized Futaki Invariant I
• On Isolated Rational Singularities of Surfaces
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
• Compact moduli of plane curves
• Existence of minimal models for varieties of log general type