Henri Guenancia

activity

20102026

most citedKlt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups

47 citations · 143 across the 31 of their papers we have counts for

collaborators

40 papers

math.AG2026

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…

math.AG2026

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 $Q$ -sheaves on Kähler varieties, generalizing our earlier work \cite{GP25} in…

math.DG2025

Kähler-Ricci flows coming out of metric spaces

Alix Deruelle, Vincent Guedj, Henri Guenancia +1

Given a compact Kähler manifold $X$ and a closed, positive $(1, 1)$ -current $T$ on $X$ , we find sufficient conditions for $T$ to induce a metric structure $(X, d_{T})$ which is the Gro…

math.AG2025

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…

math.DG2025

A note on orbifold regularity of canonical metrics

Henri Guenancia, Chung-Ming Pan, Mihai Păun

In this short note, we prove that on a compact Kähler variety $X$ with log terminal singularities and $c_{1} (X) = 0$ , any singular Ricci-flat Kähler metric has orbifold singularities i…

math.AG2025

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 $(X, D)$ such that $K_{X} + D = 0$ . More specifically, we focus on the two cases where $X$ is a Fa…

math.DG2025

Kähler-Einstein metrics of negative curvature

Henri Guenancia, Ursula Hamenstädt

Given any integer $n \geq 2$ , we construct a compact Kähler-Einstein manifold of dimension n of negative sectional curvature which is not covered by the ball.

math.DG2024

Degenerating conic Kähler-Einstein metrics to the normal cone

Olivier Biquard, Henri Guenancia

Let $X$ be a Fano manifold of dimension at least $2$ and $D$ be a smooth divisor in a multiple of the anticanonical class, $\frac{1}{α} (- K_{X})$ with $α > 1$ . It is well-known that Kähler-…

math.AG2024

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…

math.DG2023

Diameter of Kähler currents

Vincent Guedj, Henri Guenancia, Ahmed Zeriahi

We establish upper bounds on the diameter of compact Kähler manifolds endowed with Kähler metrics whose volume form satisfies an Orlicz integrability condition. Our results extend…

math.DG2023

Geometry of $K$ -trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures

Indranil Biswas, Junyan Cao, Sorin Dumitrescu +1

Let $X$ be a compact complex manifold such that its canonical bundle $K_{X}$ is numerically trivial. Assume additionally that $X$ is Moishezon or $X$ is Fujiki with dimension at most…

math.CV2023★ 1 cited

Strict positivity of Kähler-Einstein currents

Vincent Guedj, Henri Guenancia, Ahmed Zeriahi

Kähler-Einstein currents, also known as singular Kähler-Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular co…

math.AG2023★ 3 cited

Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs

Benoît Claudon, Patrick Graf, Henri Guenancia

Let $(X, Δ)$ be a compact Kähler klt pair, where $K_{X} + Δ$ is ample or numerically trivial, and $Δ$ has standard coefficients. We show that if equality holds in the orbifold Miyaok…

math.AG2021★ 5 cited

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…

math.DG2021★ 7 cited

Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric

Olivier Biquard, Henri Guenancia

Let $X$ be a complex projective manifold and let $D \subset X$ be a smooth divisor. In this article, we are interested in studying limits when $β \to 0$ of Kähler-Einstein metrics $ω…

math.CV2021

Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric

Junyan Cao, Henri Guenancia, Mihai Păun

In this note, we obtain various formulas for the curvature of the $L^{2}$ metric on the direct image of the relative canonical bundle twisted by a holomorphic line bundle endowed wit…

math.CV2020

Continuity of singular Kähler-Einstein potentials

Vincent Guedj, Henri Guenancia, Ahmed Zeriahi

In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Ampère equations (DCMAE) on singular spaces. First, we study the Dirichlet problem fo…

math.AG2020

Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties

Benjamin Bakker, Henri Guenancia, Christian Lehn

We extend the decomposition theorem for numerically $K$ -trivial varieties with log terminal singularities to the Kähler setting. Along the way we prove that all such varieties admi…

math.AG2020★ 1 cited

A decomposition theorem for $Q$ -Fano Kähler-Einstein varieties

Stéphane Druel, Henri Guenancia, Mihai Păun

Let $X$ be a $Q$ -Fano variety admitting a Kähler-Einstein metric. We prove that up to a finite quasi-étale cover, $X$ splits isometrically as a product of Kähler-Einstein $…

math.AG2020★ 10 cited

Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups

Benoît Claudon, Patrick Graf, Henri Guenancia +1

Let $X$ 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 $X$ : any suc…

math.CV2020

Families of singular Kähler-Einstein metrics

Eleonora Di Nezza, Vincent Guedj, Henri Guenancia

Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Kähler manifolds, that allo…

math.DG2019★ 2 cited

Variation of singular Kähler-Einstein metrics: Kodaira dimension zero

Junyan Cao, Henri Guenancia, Mihai Păun

We study several questions involving relative Ricci-flat Kähler metrics for families of log Calabi-Yau manifolds. Our main result states that if $p : (X, B) \to Y$ is a Kähler fiber sp…

math.AG2019★ 5 cited

On subvarieties of singular quotients of bounded domains

Benoît Cadorel, Simone Diverio, Henri Guenancia

Let $X$ be a quotient of a bounded domain in $C^{n}$ . Under suitable assumptions, we prove that every subvariety of $X$ not included in the branch locus of the quotient map i…

math.DG2019

A Bochner principle and its applications to Fujiki class $C$ manifolds with vanishing first Chern class

Indranil Biswas, Sorin Dumitrescu, Henri Guenancia

We prove a Bochner type vanishing theorem for compact complex manifolds $Y$ in Fujiki class $C$ , with vanishing first Chern class, that admit a cohomology class $[α] \in H…

Stable Degeneration, Non-degenerate Forms, and Kaledin's Conjecture

A complex analytic approach to orbifold Chern classes on singular varieties and its applications

Kähler-Ricci flows coming out of metric spaces

Beauville-Bogomolov decomposition for klt varieties

A note on orbifold regularity of canonical metrics

Log Calabi--Yau manifolds: holomorphic tensors, stability and universal cover

Kähler-Einstein metrics of negative curvature

Degenerating conic Kähler-Einstein metrics to the normal cone

Bogomolov-Gieseker inequality for log terminal Kähler threefolds

Diameter of Kähler currents

Geometry of K-trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures

Strict positivity of Kähler-Einstein currents

Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs

Numerical characterization of complex torus quotients

Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric

Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric

Continuity of singular Kähler-Einstein potentials

Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties

A decomposition theorem for Q-Fano Kähler-Einstein varieties

Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups

Families of singular Kähler-Einstein metrics

Variation of singular Kähler-Einstein metrics: Kodaira dimension zero

On subvarieties of singular quotients of bounded domains

A Bochner principle and its applications to Fujiki class C manifolds with vanishing first Chern class

Geometry of $K$ -trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures

A decomposition theorem for $Q$ -Fano Kähler-Einstein varieties

A Bochner principle and its applications to Fujiki class $C$ manifolds with vanishing first Chern class