2024/05/13 by Yuji Odaka, Odaka, Yuji · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Calabi–Yau manifold #Einstein #Geometry and complex manifolds #Mathematical analysis #Mathematical physics #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Quantum mechanics
paper · pdf · doi:10.48550/arxiv.2405.07939
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct proper moduli algebraic spaces of K-polystable ℚ-Fano cones (a.k.a. Calabi-Yau cones) or equivalently their links i.e., Sasaki-Einstein manifolds with singularities. As a byproduct, it gives alternative algebraic construction of proper K-moduli of ℚ-Fano varieties. In contrast to the previous algebraic proof of its properness ([BHLLX, LXZ]), we do not use the δ-invariants ([FO, BJ]) nor the L2-normalized Donaldson-Futaki invariants. We use the local normalized volume of [Li] and the higher Θ-stable reduction instead.