21 citations · 123 across the 34 of their papers we have counts for
39 papers
On rational chain connectedness of globally +-regular varieties
Emre Alp Özavcı, Zsolt Patakfalvi, Kevin Tucker +2
We prove that globally -regular varieties are rationally chain connected in dimension three and mixed characteristic with residue field characteristic . We also introduce a…
On surfaces with smooth projective models over
Fabio Bernasconi, Gebhard Martin, Zsolt Patakfalvi
In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over and over more general rin…
Effective positivity of Hodge bundles and applications
Giulio Codogni, Zsolt Patakfalvi, Luca Tasin
We prove new boundedness results across different areas of algebraic geometry, stemming from a unifying technical starting point: bounding the integer such that the -th…
On Gorenstein -rational threefold and fourfold singularities
Jefferson Baudin, Zsolt Patakfalvi, Linus Rösler +1
We prove that for and , quasi--Gorenstein --pure and --rational --fold singularities are canonical. This is analogous to the usual fact that r…
Perfectoid pure singularities
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +4
Fix a prime number . Inspired by the notion of -pure or -split singularities, we study the condition that a Noetherian ring with in its Jacobson radical is pure inside…
A strong counterexample to the log canonical Beauville--Bogomolov decomposition
Fabio Bernasconi, Stefano Filipazzi, Zsolt Patakfalvi +1
For every , we construct a -dimensional, log canonical, -trivial variety with the property that two general fibers of its Albanese morphism are not birational. This…
Test ideals in mixed characteristic: a unified theory up to perturbation
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +5
Let be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inver…
The Demailly--Peternell--Schneider conjecture is true in positive characteristic
Sho Ejiri, Zsolt Patakfalvi
We prove the Demailly--Peternell--Schneider conjecture in positive characteristic: if is a smooth projective variety over an algebraically closed field of characteristic …
On the properness of the moduli space of stable surfaces over
Emelie Arvidsson, Fabio Bernasconi, Zsolt Patakfalvi
We show the properness of the moduli stack of stable surfaces over , assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local…
Varieties with ample Frobenius-trace kernel
Javier Carvajal-Rojas, Zsolt Patakfalvi
In the search of a projective analog of Kunz's theorem and a Frobenius-theoretic analog of Mori--Hartshorne's theorem, we investigate the positivity of the kernel of the Frobenius…
Wall crossing for moduli of stable log pairs
Kenneth Ascher, Dori Bejleri, Giovanni Inchiostro +1
We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients o…
A note on families of K-semistable log-Fano pairs
Giulio Codogni, Zsolt Patakfalvi
In this short note, we give an alternative proof of the semipositivity of the Chow-Mumford line bundle for families of K-semistable log-Fano pairs, and of the nefness threeshold fo…
Generic vanishing in characteristic p>0 and the geometry of theta divisors
Christopher D. Hacon, Zsolt Patakfalvi
In this paper we prove a strengthening of the generic vanishing result in characteristic given in [HP16]. As a consequence of this result, we show that irreducible diviso…
Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic
Zsolt Patakfalvi
We show that if is a surjective morphism between smooth projective varieties over an algebraically closed field of characteristic with geometrically int…
Ordinary varieties with trivial canonical bundle are not uniruled
Zsolt Patakfalvi, Maciej Zdanowicz
We prove that smooth, projective, -trivial, weakly ordinary varieties over a perfect field of characteristic are not geometrically uniruled. We also show a singular versio…
The weak Beauville--Bogomolov decomposition in characteristic
Zsolt Patakfalvi, Maciej Zdanowicz
We prove a variant of the Beauville--Bogomolov decomposition for weakly ordinary, or generally globally -split, varieties with , in characteristic . We also…
Positivity of the CM line bundle for families of K-stable klt Fano varieties
Giulio Codogni, Zsolt Patakfalvi
The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space o…
On the projectivity of the moduli space of stable surfaces in characteristic p>5
Zsolt Patakfalvi
We prove that every proper subspace of the moduli space of stable surfaces with fixed volume over an algebraically closed field of characteristic p>5 is projective. As a consequenc…
Singularities of General Fibers and the LMMP
Zsolt Patakfalvi, Joe Waldron
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to…
Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0
Christopher D. Hacon, Zsolt Patakfalvi, Lei Zhang
Let be an algebraically closed field of characteristic . We give a birational characterization of ordinary abelian varieties over : a smooth projective variety is b…
Frobenius techniques in birational geometry
Zsolt Patakfalvi
This is a survey for the 2015 AMS Summer Institute on Algebraic Geometry about the Frobenius type techniques recently used extensively in positive characteristic algebraic geometry…
On the characterization of abelian varieties in characteristic
Christopher Hacon, Zsolt Patakfalvi
This article is superseded by 1703.06631. We keep this version here since some of the arguments for the special cases treated here are different than those of 1703.06631.
Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension
Sándor J Kovács, Zsolt Patakfalvi
We prove a strengthening of Kollár's Ampleness Lemma and use it to prove that any proper coarse moduli space of stable log-varieties of general type is projective. We also prove su…
Ampleness of the CM line bundle on the moduli space of canonically polarized varieties
Zsolt Patakfalvi, Chenyang Xu
We prove that the CM line bundle is ample on the proper moduli space which parametrizes KSBA stable varieties.