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

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.

References in corpus (3)

• Moduli of varieties of general type
• Calabi-Yau manifolds with isolated conical singularities
• K-stability of Fano manifolds with not small alpha invariants

Cited by in corpus (6)

• Birational superrigidity and K-stability of singular Fano complete intersections
• Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)
• Stability of Valuations: Higher Rational Rank
• Applications of the moduli continuity method to log K-stable pairs
• The moduli space of Fano manifolds with Kähler-Ricci solitons
• On the semi-continuity problem of normalized volumes of singularities