A tower of complete moduli spaces of Calabi-Yau n-folds

2025/11/20 by Alexeev, Valery
#14B07 #14D23 #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.16562

Abstract

We generalize to dimensions n≥3 the compactified moduli stack of elliptic curves M_1,1=ℙ(4,6) and Brieskorn's family of U⊕~E₈-polarized K3 surfaces over a 10-dimensional weighted projective space.

Citations

• Smooth Calabi-Yau varieties with large index and Betti numbers
• Calabi-Yau varieties of large index
• Varieties of general type with doubly exponential asymptotics
• Multiplier Ideals of Sufficiently General Polynomials
• Multiplier Ideals of Monomial Ideals
• Hypersurface exceptional singularities
• Log canonical singularities and complete moduli of stable pairs

Related

• Polarized Calabi-Yau 3-folds in codimension 4
• Good moduli spaces for boundary polarized Calabi-Yau surface pairs
• K-moduli of Fano threefolds and genus four curves
• Complete curves in the moduli space of polarized K3 surfaces and hyper-Kähler manifolds
• Calabi-Yau Three-folds and Moduli of Abelian Surfaces II