47 citations · 143 across the 31 of their papers we have counts for
15 papers · 1 filter
Stable Degeneration, Non-degenerate Forms, and Kaledin's Conjecture
Chenyang Xu, Ziquan Zhuang, Henri Guenancia
We prove that stable degeneration, the canonical degeneration associated to the normalized volume minimizer of a Kawamata log terminal (klt) singularity, preserves non-degenerate r…
A complex analytic approach to orbifold Chern classes on singular varieties and its applications
Henri Guenancia, Mihai Păun
In this article, we prove the orbifold version of the Bogomolov-Gieseker inequality for stable -sheaves on Kähler varieties, generalizing our earlier work \cite{GP25} in…
Beauville-Bogomolov decomposition for klt varieties
Henri Guenancia
These lecture notes present a mostly self-contained proof of the singular version of Beauville-Bogomolov decomposition theorem for compact Kähler varieties with log terminal singul…
Log Calabi--Yau manifolds: holomorphic tensors, stability and universal cover
Tristan C. Collins, Henri Guenancia
We study various geometric properties of log Calabi-Yau manifolds, i.e. log smooth pairs such that . More specifically, we focus on the two cases where is a Fa…
Bogomolov-Gieseker inequality for log terminal Kähler threefolds
Henri Guenancia, Mihai Păun
In this article we are mainly concerned with three dimensional compact Kähler spaces with log terminal singularities. We establish the orbifold version of the Bogomolov-Gieseker in…
Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
Benoît Claudon, Patrick Graf, Henri Guenancia
Let be a compact Kähler klt pair, where is ample or numerically trivial, and has standard coefficients. We show that if equality holds in the orbifold Miyaok…
Numerical characterization of complex torus quotients
Benoît Claudon, Patrick Graf, Henri Guenancia
This article gives a characterization of quotients of complex tori by finite groups acting freely in codimension two in terms of a numerical vanishing condition on the first and se…
Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties
Benjamin Bakker, Henri Guenancia, Christian Lehn
We extend the decomposition theorem for numerically -trivial varieties with log terminal singularities to the Kähler setting. Along the way we prove that all such varieties admi…
A decomposition theorem for -Fano Kähler-Einstein varieties
Stéphane Druel, Henri Guenancia, Mihai Păun
Let be a -Fano variety admitting a Kähler-Einstein metric. We prove that up to a finite quasi-étale cover, splits isometrically as a product of Kähler-Einstein $…
Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups
Benoît Claudon, Patrick Graf, Henri Guenancia +1
Let be a compact Kähler space with klt singularities and vanishing first Chern class. We prove the Bochner principle for holomorphic tensors on the smooth locus of : any suc…
On subvarieties of singular quotients of bounded domains
Benoît Cadorel, Simone Diverio, Henri Guenancia
Let be a quotient of a bounded domain in . Under suitable assumptions, we prove that every subvariety of not included in the branch locus of the quotient map i…
A decomposition theorem for smoothable varieties with trivial canonical class
Stéphane Druel, Henri Guenancia
In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cove…
Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
Daniel Greb, Henri Guenancia, Stefan Kebekus
We investigate the holonomy group of singular Kähler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components,…
Orbifold Stability and Miyaoka-Yau Inequality for minimal pairs
Henri Guenancia, Behrouz Taji
After establishing suitable notions of stability and Chern classes for singular pairs, we use Kähler-Einstein metrics with conical and cuspidal singularities to prove the slope sem…
Semi-stability of the tangent sheaf of singular varieties
Henri Guenancia
The main goal of this paper is to prove the polystability of the logarithmic tangent sheaf of a log canonical pair whose canonical bundle is ampl…