Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability

Abstract

In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for $d=2,3,4$, these K-moduli of pairs are isomorphic to the K-moduli spaces of del Pezzo surfaces. For $d=1$, we prove that they are different by exhibiting some walls.

arXiv commentTo appear in Canadian Journal of Mathematics

References in corpus (9)

• K-semistability is equivariant volume minimization
• Stable pair, tropical, and log canonical compact moduli of del Pezzo surfaces
• Optimal destabilizing centers and equivariant K-stability
• Reductivity of the automorphism group of K-polystable Fano varieties
• The volume of singular Kähler-Einstein Fano varieties
• On positivity of the CM line bundle on K-moduli spaces
• On K-stability of finite covers
• CM Stability And The Generalized Futaki Invariant II
• A Minimizing Valuation is Quasi-monomial