105 citations · 275 across the 27 of their papers we have counts for
28 papers
Minimization of Arakelov K-energy for many cases
Masafumi Hattori, Yuji Odaka
We prove that for various polarized varieties over , which broadly includes K-trivial case, K-ample case, Fano case, minimal models, certain classes of fibra…
Special Lagrangian fibrations, Berkovich retraction, and crystallographic groups
Keita Goto, Yuji Odaka
We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties, glue with Berkovich retraction in non-Archimedean geometry by…
Semi-toric and toroidal compactifications as log minimal models, and applications to weak K-moduli
Yuji Odaka
We give a characterization of toroidal (resp., semi-toric) compactifications due to Ash-Mumford-Rapoport-Tai (resp., Looijenga) as log minimal models and apply it to study weak K-m…
On log minimality of weak K-moduli compactifications of Calabi-Yau varieties
Yuji Odaka
For moduli of polarized smooth K-trivial a.k.a., Calabi-Yau varieties in a general sense, we revisit a classical problem of constructing its "weak K-moduli" compactifications which…
Fano Shimura varieties with mostly branched cusps
Yota Maeda, Yuji Odaka
We prove that the Satake-Baily-Borel compactification of certain Shimura varieties are Fano varieties, Calabi-Yau varieties or have ample canonical divisors with mild singularities…
Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
Yuji Odaka
For any degenerating Calabi-Yau family, we introduce new limit space which we call galaxy, whose dense subspace is the disjoint union of countably infinite open Calabi-Yau varietie…
PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
Yuji Odaka
A protagonist here is a new-type invariant for type II degenerations of K3 surfaces, which is explicit PL (piecewise linear) convex function from the interval with at most 18 non-l…
Polystable log Calabi-Yau varieties and Gravitational instantons
Yuji Odaka
Open Calabi-Yau manifolds and log Calabi-Yau varieties have been broadly studied over decades. Regarding them as "semistable" objects, we propose to consider their good proper subc…
Collapsing K3 surfaces, Tropical geometry and Moduli compactifications of Satake, Morgan-Shalen type
Yuji Odaka, Yoshiki Oshima
We provide a moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics via compactification of moduli varieties of Morgan-Shalen and Satake type. In patricular, we…
Collapsing K3 Surfaces and Moduli Compactification
Yuji Odaka, Yoshiki Oshima
This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study espe…
Tropical Geometric Compactification of Moduli, II - case and holomorphic limits -
Yuji Odaka
We compactify the classical moduli variety of principally polarized abelian varieties of complex dimension by attaching the moduli of flat tori of real dimensions at most…
On the K-stability of Fano varieties and anticanonical divisors
Kento Fujita, Yuji Odaka
We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition…
Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
Yuji Odaka
We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program,…
Compact moduli space of Kahler-Einstein Fano varieties
Yuji Odaka
We construct a geometrically compactified moduli algebraic space of Kahler-Einstein Fano manifolds.
Invariants of Varieties and Singularities inspired by Kahler-Einstein problems
Yuji Odaka
We extend the framework of K-stability (Tian, Donaldson) to more general algebro-geometric setting, such as partial desingularisations of (fixed) singularities, (not necessarily fl…
Tropical Geometric Compactification of Moduli, I - case -
Yuji Odaka
We compactify the classical moduli variety of compact Riemann surfaces by attaching moduli of (metrized) graphs as boundary. The compactifications do not admit the structure of var…
Separatedness of moduli of K-stable varieties
Yuji Odaka, Richard P Thomas
Given a one parameter flat family of polarized algebraic varieties, we show that any K-stable limit is unique. In particular, moduli spaces of K-stable polarized varieties are auto…
On the moduli of Kahler-Einstein Fano manifolds
Yuji Odaka
We prove that Kahler-Einstein Fano manifolds with finite automorphism groups form Hausdorff moduli algebraic space with only quotient singularities. We also discuss the limits as Q…
Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
Yuji Odaka, Cristiano Spotti, Song Sun
We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification.…
On parametrization, optimization and triviality of test configurations
Yuji Odaka
We give a parametrization of test configurations in the sense of Donaldson via spherical buildings, and show the existence of "optimal" destabilizing test configurations for unstab…
Testing log K-stability by blowing up formalism
Yuji Odaka, Song Sun
We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results…
Log-canonical models of singular pairs and its applications
Yuji Odaka, Chenyang Xu
We prove the existence of log canonical modifications for a log pair. As an application, together with Kollär's gluing theory, we remove the assumption in the first named author's…
Birational superrigidity and slope stability of Fano manifolds
Yuji Odaka, Takuzo Okada
We show a relation between the birational superrigidity of Fano manifold and its slope stability in the sense of Ross-Thomas.
Alpha invariant and K-stability of Q-Fano varieties
Yuji Odaka, Yuji Sano
We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a…