The stability threshold and Diophantine approximation

DOI10.1090/bproc/64zbMath1485.14073OpenAlexW4229081406MaRDI QIDQ5075997

Yan He, Min Ru

Publication date: 12 May 2022

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/bproc/64

zbMATH Keywords

Ru-Vojta's theorem

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Fano varieties (14J45) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97) Value distribution theory in higher dimensions (32H30) Schmidt Subspace Theorem and applications (11J87)

Related Items (2)

Expectations, concave transforms, Chow weights and Roth's theorem for varieties ⋮ Complex geometry and dynamical systems. Abstracts from the workshop held September 4--10, 2022

Cites Work

• Unnamed Item
• Unnamed Item
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• An analogue of Liouville's theorem and an application to cubic surfaces
• On the nondensity of integral points
• On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
• Kähler-Einstein metrics and the generalized Futaki invariant
• Kähler-Einstein metrics with positive scalar curvature
• K-semistability is equivariant volume minimization
• Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs
• On the K-stability of Fano varieties and anticanonical divisors
• Scalar curvature and stability of toric varieties.
• Special test configuration and \(K\)-stability of Fano varieties
• Thresholds, valuations, and K-stability
• Vanishing sequences and Okounkov bodies
• Seshadri constants, Diophantine approximation, and Roth's theorem for arbitrary varieties
• A valuative criterion for uniform K-stability of \(\mathbb{Q}\)-Fano varieties
• A birational Nevanlinna constant and its consequences
• Log canonical thresholds of smooth Fano threefolds
• Convex bodies associated to linear series
• Okounkov bodies of filtered linear series
• On K-stability and the volume functions of ℚ-Fano varieties: Table 1.
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
• A generalized Schmidt subspace theorem for closed subschemes

This page was built for publication: The stability threshold and Diophantine approximation