University of Bayreuth

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19922026

most citedThe World of the Complex Ginzburg-Landau Equation

2k citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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192 papers · 1 filter

math.AG2026

Genus $2$ pencils on surfaces with $p_{g} = K^{2} = 1$ , envelopes, and conics tangent to plane cubic curves

Fabrizio Catanese, Noah Ruhland

We consider $(1, 1)$ -surfaces, namely, minimal compact complex surfaces $S$ with $p_{g} (S) = K_{S}^{2} = 1$ : for these the bicanonical map is a covering of degree $4$ of the plane $P^{2}$ . An…

math.AG2026

Mok tensors and Orbifold Quotients of Bounded symmetric domains without ball factors

Fabrizio Catanese, Marco Franciosi

In this paper we characterize the compact orbifolds, quotients $X = D /Γ$ of a bounded symmetric domain $D$ with no higher dimensional ball factor by the actio…

math.AG2026

Cohomologically or numerically trivial automorphisms of surfaces of general type

Fabrizio Catanese, Davide Frapporti

Our main result is the determination of the respective groups $A u t_{Z} (S)$ of cohomologically trivial automorphisms and $A u t_{Q} (S)$ of numerically trivial automo…

math.AG2025

Irrational pencils, and characterization of Varieties isogenous to a product, via the Profinite completion of the Fundamental group

Fabrizio Catanese, appendix by Pavel Zalesskii

We give a very short proof of two Theorems, whose content is outlined in the title, and where $Π_{g}$ is the fundamental group of a compact complex curve of genus $g$ : (1) Theorem 2.…

math.AG2025★ 1 cited

Semispecial tensors and quotients of the polydisc

Patrick Graf, Aryaman Patel

Let $X$ be a complex-projective variety with klt singularities and ample canonical divisor. We prove that $X$ is a quotient of the polydisc by a group acting properly discontinuous…

math.AG2025

Odd fake $Q$ -homology quadrics exist

Fabrizio Catanese

We show the existence of odd fake $Q$ -homology quadrics, namely of minimal surfaces $S$ of general type which have the same $Q$ -homology as a smooth quadric $Q \c…

math.AG2025

Compactification of homology cells, Fujita's conjectures and the complex projective space

Ping Li, Thomas Peternell

We show that a compact Kähler manifold $M$ containing a smooth connected divisor $D$ such that $M ∖ D$ is a homology cell, e.g., contractible, must be projective space with…

math.AG2025★ 1 cited

Mori dream spaces and Q-homology quadrics

Paolo Cascini, Fabrizio Catanese, Yifan Chen +1

We show that Shavel type surfaces are fake quadrics of even type which are not Mori dream surfaces, yet there are infinitely many primes $p$ such that the reduction modulo $p$ is a…

math.AG2024

On the numerically and cohomologically trivial automorphisms of elliptic surfaces II: $χ (S) > 0$

Fabrizio Catanese, Wenfei Liu, Matthias Schütt

In this second part we study first the group $A u t_{Q} (S)$ of numerically trivial automorphisms of an algebraic properly elliptic surface $S$ , that is, of a minimal algebrai…

math.AG2024

Orbifold Quotients of Symmetric Domains of Tube type

Fabrizio Catanese

In this paper we characterize the compact orbifolds, quotients $X = D /Γ$ of a bounded symmetric domain $D$ of tube type by the action of a discontinuous grou…

math.AG2024

Orbifold Classifying Spaces and Quotients of complex Tori

Fabrizio Catanese

In this paper we characterize the quotients $X = T / G$ of a complex torus $T$ by the action of a finite group $G$ as the Kähler orbifold classifying spaces of the even Euclidean cr…

math.AG2023★ 1 cited

Miyaoka-Yau inequalities and the topological characterization of certain klt varieties

Daniel Greb, Stefan Kebekus, Thomas Peternell

Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka-Yau inequality becomes an equality. Ball…

math.AG2023

General birationality and Hyperelliptic Theta divisors

Fabrizio Catanese

We first state a condition ensuring that having a birational map onto the image is an open property for families of irreducible normal non uniruled varieties. We give then some cri…

math.AG2023

Geometric Endomorphisms of the Hesse moduli space of elliptic curves

Fabrizio Catanese, Edoardo Sernesi

We consider the geometric map $C$ , called Cayleyan, associating to a plane cubic $E$ the adjoint of its dual curve. We show that $C$ and the classical Hessian…

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.AG2023

Manifolds with trivial Chern classes II: Manifolds Isogenous to a Torus Product, coframed Manifolds and a question by Baldassarri

Fabrizio Catanese

Motivated by a general question addressed by Mario Baldassarri in 1956, we discuss characterizations of the Pseudo-Abelian Varieties introduced by Roth, and we introduce a first ne…

math.AG2022

The Hesse pencil and polarizations of type $(1, 3)$ on Abelian surfaces

Fabrizio Catanese, Edoardo Sernesi

In this short note we prove two theorems, the first one is a sharpening of a result of Lange and Sernesi: the discriminant curve W of a general Abelian surface $A$ endowed with an…

math.AG2022

Pluricanonical Maps and the Fujita Conjecture

Fabrizio Catanese

We describe examples showing the sharpness of Fujita's conjecture on adjoint bundles also in the general type case, and use these examples to formulate related bold conjectures on…

math.AG2022

Singularities of normal quartic surfaces III (char=2, non-supersingular)

Fabrizio Catanese, Matthias Schütt

We show that the maximal number of singular points of a normal quartic surface $X \subset P_{K}^{3}$ defined over an algebraically closed field $K$ of characteristic 2 is at m…

math.AG2022

Manifolds with trivial Chern classes I: Hyperelliptic Manifolds and a question by Severi

Fabrizio Catanese

We give a negative answer to a question posed by Severi in 1951, whether the Abelian Varieties are the only projective manifolds with trivial Chern classes. By Yau' s celebrated re…

math.AG2022★ 5 cited

On the $4$ -dimensional minimal model program for Kähler varieties

Omprokash Das, Christopher Hacon, Mihai Păun

In this article we establish the following results: Let $(X, B)$ be a dlt pair, where $X$ is a $Q$ -factorial Kähler $4$ -fold -- (i) if $X$ is compact and $K_X+B\sim_{\mathb…

math.AG2022★ 11 cited

The Nonvanishing problem for varieties with nef anticanonical bundle

Vladimir Lazić, Shin-ichi Matsumura, Thomas Peternell +2

We prove that if $(X, Δ)$ is a threefold pair with mild singularities such that $- (K_{X} + Δ)$ is nef, then the numerical class of $- (K_{X} + Δ)$ is effective.

math.AG2022★ 4 cited

The Classification of Rigid Hyperelliptic Fourfolds

Andreas Demleitner, Christian Gleissner

We provide a fine classification of rigid hyperelliptic manifolds in dimension four up to biholomorphism and diffeomorphism. These manifolds are explicitly described as finite étal…

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…

Genus 2 pencils on surfaces with pg​=K2=1, envelopes, and conics tangent to plane cubic curves

Mok tensors and Orbifold Quotients of Bounded symmetric domains without ball factors

Cohomologically or numerically trivial automorphisms of surfaces of general type

Irrational pencils, and characterization of Varieties isogenous to a product, via the Profinite completion of the Fundamental group

Semispecial tensors and quotients of the polydisc

Odd fake Q -homology quadrics exist

Compactification of homology cells, Fujita's conjectures and the complex projective space

Mori dream spaces and Q-homology quadrics

On the numerically and cohomologically trivial automorphisms of elliptic surfaces II: χ(S)>0

Orbifold Quotients of Symmetric Domains of Tube type

Orbifold Classifying Spaces and Quotients of complex Tori

Miyaoka-Yau inequalities and the topological characterization of certain klt varieties

General birationality and Hyperelliptic Theta divisors

Geometric Endomorphisms of the Hesse moduli space of elliptic curves

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

Manifolds with trivial Chern classes II: Manifolds Isogenous to a Torus Product, coframed Manifolds and a question by Baldassarri

The Hesse pencil and polarizations of type (1,3) on Abelian surfaces

Pluricanonical Maps and the Fujita Conjecture

Singularities of normal quartic surfaces III (char=2, non-supersingular)

Manifolds with trivial Chern classes I: Hyperelliptic Manifolds and a question by Severi

On the 4-dimensional minimal model program for Kähler varieties

The Nonvanishing problem for varieties with nef anticanonical bundle

The Classification of Rigid Hyperelliptic Fourfolds

The Violation of the Lipman-Zariski conjecture in positive characteristic

Genus $2$ pencils on surfaces with $p_{g} = K^{2} = 1$ , envelopes, and conics tangent to plane cubic curves

Odd fake $Q$ -homology quadrics exist

On the numerically and cohomologically trivial automorphisms of elliptic surfaces II: $χ (S) > 0$

The Hesse pencil and polarizations of type $(1, 3)$ on Abelian surfaces

On the $4$ -dimensional minimal model program for Kähler varieties