37 citations · 362 across the 39 of their papers we have counts for
40 papers
Modular variants of p-adic fundamental sequence
Heng Du, Qingyuan Jiang, Yucheng Liu
In this article, we relate any Farey triangle in the extended upper half-plane to a variant of Colmez--Fontaine's fundamental lemma in -adic Hodge theory. In particular, their o…
On positivity of the limit F-signature
Yuchen Liu, Suchitra Pande
We study a conjecture of Carvajal-Rojas, Schwede and Tucker which states that for a complex KLT singularity , the F-signatures of the reductions of to charac…
Valuative independence for Calabi--Yau varieties
Harold Blum, Yuchen Liu
We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular funct…
Moduli of boundary polarized Calabi-Yau pairs
Kenneth Ascher, Dori Bejleri, Harold Blum +4
We develop the moduli theory of boundary polarized CY pairs, which are slc Calabi-Yau pairs such that is ample. The motivation for studying this moduli problem is to co…
Stability conditions on cyclic categories I: basic definitions and examples
Yucheng Liu
A triangulated category with a canonical Bott's isomorphism is called a cyclic category in this paper. We give a new notion of stability con…
Continuous-time weakly self-avoiding walk on has strictly monotone escape speed
Yucheng Liu
Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On , Greven and den Hollander proved in 1993 that the discret…
Convexity of multiplicities of filtrations on local rings
Harold Blum, Yuchen Liu, Lu Qi
We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a conse…
Filtrations and torsion pairs in Abramovich Polishchuk's heart
Yucheng Liu
We study some abelian subcategories and torsion pairs in Abramovich Polishchuk's heart. And we construct stability conditions on a full triangulated subcategory $\mathcal{D}^{\leq…
On the boundedness of singularities via normalized volume
Yuchen Liu, Joaquín Moraga, Hendrik Süß
In this article we study conjectures regarding normalized volume and boundedness of singularities. We focus on singularities with a torus action of complexity 1, threefold singular…
K-stability of Fano threefolds of rank 2 and degree 14 as double covers
Yuchen Liu
We prove that every smooth Fano threefold from the family No 2.8 is K-stable. Such a Fano threefold is a double cover of the blow-up of at one point branched along a…
Infinitely many families of Sasaki-Einstein metrics on spheres
Yuchen Liu, Taro Sano, Luca Tasin
We show that there exist infinitely many families of Sasaki-Einstein metrics on every odd-dimensional standard sphere of dimension at least . We also show that the same result i…
K-stability and birational models of moduli of quartic K3 surfaces
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We show that the K-moduli spaces of log Fano pairs where is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Bo…
The existence of the Kähler-Ricci soliton degeneration
Harold Blum, Yuchen Liu, Chenyang Xu +1
We prove an algebraic version of the Hamilton-Tian Conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a r…
Finite generation for valuations computing stability thresholds and applications to K-stability
Yuchen Liu, Chenyang Xu, Ziquan Zhuang
We prove that on any log Fano pair of dimension whose stability threshold is less than , any valuation computing the stability threshold has a finitely generated…
ACC for local volumes and boundedness of singularities
Jingjun Han, Yuchen Liu, Lu Qi
The ACC conjecture for local volumes predicts that the set of local volumes of klt singularities satisfies the ACC if the coefficients of belong to a DCC set. In t…
On K-stability of some del Pezzo surfaces of Fano index 2
Yuchen Liu, Andrea Petracci
For every integer , we relate the K-stability of hypersurfaces in the weighted projective space of degree with the GIT stability of binary form…
On properness of K-moduli spaces and optimal degenerations of Fano varieties
Harold Blum, Daniel Halpern-Leistner, Yuchen Liu +1
We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable…
Some quadratic inequalities on product varieties
Yucheng Liu
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability c…
K-stability of cubic fourfolds
Yuchen Liu
We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the correspond…
K-moduli of curves on a quadric surface and K3 surfaces
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We show that the K-moduli spaces of log Fano pairs where is a -curve and their wall crossings coincide with the VGIT quotients of…
Equivariant K-stability under finite group action
Yuchen Liu, Ziwen Zhu
We show that G-equivariant K-semistability (resp. G-equivariant K-polystability) implies K-semistability (resp. K-polystability) for log Fano pairs when G is a finite group.
Wall crossing for K-moduli spaces of plane curves
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We construct proper good moduli spaces parametrizing K-polystable -Gorenstein smoothable log Fano pairs , where is a Fano variety and is a rational mul…
On the Cheltsov--Rubinstein conjecture
Kento Fujita, Yuchen Liu, Hendrik Süß +2
In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.
Stability conditions on product varieties
Yucheng Liu
Given a stability condition on a smooth projective variety , we construct a family of stability conditions on , where is a smooth projective curve. In particular,…