Year: 2026
Type: preprint
Abstract: Let $(X, Ω)$ be an affine Calabi--Yau variety, by which we mean a klt affine variety $X$ with a non-vanishing algebraic volume form $Ω$. In connection with complete Calabi--Yau metrics of Euclidean volume growth on $(X, Ω)$, we study algebraic aspects of polarizations of $X$ given by a negative valuation. We show that such a valuation is finitely generated with a klt degeneration if and only if $X$ admits a dlt log Fano type compactification, generalizing a compactification considered by Tian--Yau. We further give a valuative criterion detecting K-semistability of the degeneration by a negative valuation.
Source: arXiv (Cornell University)
Author: Wu, Yueqiao
Institution: Johns Hopkins University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: Research in Mathematics
OpenAlex ID: W7223690474