Patrick Graf

activity

20122023

most citedAlgebraic approximation of Kähler threefolds of Kodaira dimension zero

16 citations · 104 across the 22 of their papers we have counts for

collaborators

22 papers

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.DG2023★ 1 cited

Hermite--Einstein metrics in singular settings

Junyan Cao, Patrick Graf, Philipp Naumann +3

In this article we pursue the following main goals. In the first place, we establish the existence of "estimable" Hermite--Einstein metrics for stable reflexive coherent sheaves on…

math.AG2022

The Violation of the Lipman-Zariski conjecture in positive characteristic

Patrick Graf

We study the failure of the Lipman-Zariski conjecture in positive characteristic. For rational double points, the conjecture holds true except for a short finite list of exceptions…

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.AG2021

A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four

Patrick Graf

Let $X$ be a compact Kähler fourfold with klt singularities and vanishing first Chern class, smooth in codimension two. We show that $X$ admits a Beauville-Bogomolov decomposition:…

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.AG2020★ 2 cited

The Kodaira problem for Kähler spaces with vanishing first Chern class

Patrick Graf, Martin Schwald

Let $X$ be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that $X$ admits arbitrarily small deformations that are projective varieties i…

math.AG2019

A note on Flenner's extension theorem

Patrick Graf

We show that any $p$ -form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as long as $p \le \mathrm{codim}_…

math.AG2019★ 11 cited

Differential forms on log canonical spaces in positive characteristic

Patrick Graf

Given a logarithmic $1$ -form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \geq 7$ , we show that it extends with at worst logar…

math.AG2019★ 2 cited

The Lipman-Zariski conjecture in genus one higher

Hannah Bergner, Patrick Graf

We prove the Lipman-Zariski conjecture for complex surface singularities with $p_{g} - g - b \leq 2$ . Here $p_{g}$ is the geometric genus, $g$ is the sum of the genera of the exceptiona…

math.AG2018★ 6 cited

On the Kodaira problem for uniruled Kähler spaces

Patrick Graf, Martin Schwald

We discuss the Kodaira problem for uniruled Kähler spaces. Building on a construction due to Voisin, we give an example of a uniruled Kähler space $X$ such that every run of the $K…

math.AG2018★ 2 cited

The Lipman-Zariski conjecture in low genus

Patrick Graf

We prove the Lipman-Zariski conjecture for complex surface singularities of genus one, and also for those of genus two whose link is not a rational homology sphere. As an applicati…

math.AG2017★ 12 cited

Finite quotients of three-dimensional complex tori

Patrick Graf, Tim Kirschner

We provide a characterization of quotients of three-dimensional complex tori by finite groups that act freely in codimension one via a vanishing condition on the first and second o…

math.AG2016★ 9 cited

Étale fundamental groups of strongly $F$ -regular schemes

Bhargav Bhatt, Javier Carvajal-Rojas, Patrick Graf +2

We prove that a strongly $F$ -regular scheme $X$ admits a finite, generically Galois, and étale-in-codimension-one cover $X \to X$ such that the étale fundamental groups…

math.AG2016

Discreteness of $F$ -jumping numbers at isolated non-Q-Gorenstein points

Patrick Graf, Karl Schwede

We show that the $F$ -jumping numbers of a pair $(X, a)$ in positive characteristic have no limit points whenever the symbolic Rees algebra of $- K_{X}$ is finitely generated…

math.AG2016★ 16 cited

Algebraic approximation of Kähler threefolds of Kodaira dimension zero

Patrick Graf

We prove that for a compact Kähler threefold with canonical singularities and vanishing first Chern class, the projective fibres are dense in the semiuniversal deformation space. T…

math.AG2015★ 3 cited

A Mehta-Ramanathan theorem for linear systems with basepoints

Patrick Graf

Let $(X, H)$ be a normal complex projective polarized variety and $E$ an $H$ -semistable sheaf on $X$ . We prove that the restriction $E_{C}$ to a sufficiently p…

math.AG2014★ 2 cited

The jumping coefficients of non-Q-Gorenstein multiplier ideals

Patrick Graf

Let $a \subset O_{X}$ be a coherent ideal sheaf on a normal complex variety $X$ , and let $c \geq 0$ be a real number. De Fernex and Hacon associated a multiplier id…

math.AG2014★ 5 cited

The generalized Lipman-Zariski problem

Patrick Graf

We propose and study a generalized version of the Lipman-Zariski conjecture: let $(x \in X)$ be an $n$ -dimensional singularity such that for some integer $1 \leq p \leq n - 1$ , the s…

math.AG2014★ 4 cited

Potentially Du Bois spaces

Patrick Graf, Sándor J Kovács

We investigate properties of potentially Du Bois singularities, that is, those that occur on the underlying space of a Du Bois pair. We show that a normal variety $X$ with potentia…

math.AG2013

An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture

Patrick Graf, Sándor J Kovács

Let $X$ be a normal variety. Assume that for some reduced divisor $D \subset X$ , logarithmic 1-forms defined on the snc locus of $(X, D)$ extend to a log resolution $\tilde X \to X…

math.AG2012★ 11 cited

Bogomolov-Sommese vanishing on log canonical pairs

Patrick Graf

Let (X, D) be a projective log canonical pair. We show that for any natural number p, the sheaf (Omega_X^p(log D))^** of reflexive logarithmic p-forms does not contain a Weil divis…

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

Hermite--Einstein metrics in singular settings

The Violation of the Lipman-Zariski conjecture in positive characteristic

Numerical characterization of complex torus quotients

A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four

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

The Kodaira problem for Kähler spaces with vanishing first Chern class

A note on Flenner's extension theorem

Differential forms on log canonical spaces in positive characteristic

The Lipman-Zariski conjecture in genus one higher

On the Kodaira problem for uniruled Kähler spaces

The Lipman-Zariski conjecture in low genus

Finite quotients of three-dimensional complex tori

Étale fundamental groups of strongly F-regular schemes

Discreteness of F-jumping numbers at isolated non-Q-Gorenstein points

Algebraic approximation of Kähler threefolds of Kodaira dimension zero

A Mehta-Ramanathan theorem for linear systems with basepoints

The jumping coefficients of non-Q-Gorenstein multiplier ideals

The generalized Lipman-Zariski problem

Potentially Du Bois spaces

An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture

Bogomolov-Sommese vanishing on log canonical pairs

Étale fundamental groups of strongly $F$ -regular schemes

Discreteness of $F$ -jumping numbers at isolated non-Q-Gorenstein points