On the moduli of Kahler-Einstein Fano manifolds

Abstract

We prove that Kahler-Einstein Fano manifolds with finite automorphism groups form Hausdorff moduli algebraic space with only quotient singularities. We also discuss the limits as Q-Fano varieties which should be put on the boundary of its canonical compactification.

15 pages. Final version appeared in Proceeding of Kinosaki algebraic geometry symposium 2013. (I am sorry for late upload)

References in corpus (18)

• K-stability and Kähler-Einstein metrics
• Moduli of varieties of general type
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• K-stability of constant scalar curvature polarization
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Special test configurations and $K$-stability of Fano varieties
• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
• A stronger concept of K-stability
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• Log canonical thresholds of smooth Fano threefolds. With an appendix by Jean-Pierre Demailly
• Kahler-Einstein metrics and stability
• Ricci flat Kahler metrics with edge singularities
• Nonexistence of asymptotic GIT compactification
• Testing log K-stability by blowing up formalism
• Note on K-stability of pairs
• Log canonical thresholds of del Pezzo surfaces
• Extremal metrics on del Pezzo threefolds

Cited by in corpus (22)

• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
• The normalized volume of a singularity is lower semicontinuous
• K-stability of Fano varieties: an algebro-geometric approach
• Uniqueness of K-polystable degenerations of Fano varieties
• Wall crossing for K-moduli spaces of plane curves
• Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
• On properness of K-moduli spaces and optimal degenerations of Fano varieties
• Compact moduli space of Kahler-Einstein Fano varieties
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• The moduli space of Fano manifolds with Kähler-Ricci solitons
• Polystable log Calabi-Yau varieties and Gravitational instantons
• Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
• Equivariant calculus on $\mu$-character and $\mu$K-stability of polarized schemes
• Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
• Openness of uniform K-stability in the Kähler cone
• On uniform K-stability of pairs
• Minimizing CM degree and slope stability of projective varieties
• Degeneration of Ricci-flat Calabi-Yau manifolds and its applications
• Tropical Geometric Compactification of Moduli, II - $A_g$ case and holomorphic limits -
• On log minimality of weak K-moduli compactifications of Calabi-Yau varieties
• Separatedness of moduli of K-stable varieties
• Completion of the moduli space for polarized Calabi-Yau manifolds