Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds

2017/04/30 by Spotti, Cristiano, Sun, Song · 3 citations
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.00377

Abstract

We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential applications to explicit study of moduli spaces of K-stable Fano manifolds with large anti-canonical volume. Our arguments are based on recent progress about the geometry of metric tangent cones and on related ideas about the algebro-geometric study of singularities of K-stable Fano varieties.

Cited by

• Yang-Mills energy quantization over non-collapsed degenerating Einstein manifolds and applications
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• On multiscale aspects of Kähler-Einstein metrics and algebraic geometry

Related

• Degenerations of Kähler-Einstein Fano Manifolds
• On the moduli of Kahler-Einstein Fano manifolds
• Compact moduli space of Kahler-Einstein Fano varieties
• The moduli space of Fano manifolds with Kähler-Ricci solitons
• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics