Frank Gounelas

activity

20122026

most citedRemarks on the positivity of the cotangent bundle of a K3 surface

7 citations · 17 across the 13 of their papers we have counts for

collaborators

18 papers

math.AG2026

Ramification of the moduli map for hyperplane sections of K3s and hypersurfaces

Dario Faro, Frank Gounelas

Finiteness and injectivity of the moduli morphisms $μ_{n} : ∣ n H ∣_{sm} \to M_{g_{n}}$ associated with linear systems on K3 surfaces are understood in many cases. In this…

math.AG2026

Symmetric Differentials on K3 Surfaces

Frank Gounelas, Christian Liedtke

We prove that a K3 surface over an algebraically closed field admits a nonzero global symmetric differential of positive degree if and only if the characteristic is $p = 2$ , and it i…

math.AG2026

The universal cover of the second-type locus of a cubic

Frank Gounelas

We prove that the surface of second-type lines on a general cubic fourfold has fundamental group of order two. Its universal cover, constructed by Huybrechts, is obtained by consid…

math.AG2026

Isotrivial smooth curves on surfaces

Xi Chen, Frank Gounelas

We prove that a smooth projective non-uniruled surface of Picard rank one, generated by an ample and base point free line bundle, cannot be covered by an isotrivial family of smoot…

math.AG2025

Universal Brauer-Severi varieties

Frank Gounelas, Daniel Huybrechts

We construct universal Brauer-Severi varieties of fixed period and index and study their geometry. We determine their cohomology and their Brauer and Picard groups and show that th…

math.AG2025

When is the diagonal contractible?

Xi Chen, Frank Gounelas

For a smooth projective complex variety $X$ , we study the problem of when there exists a birational morphism $X \times X \to Y$ to a projective variety $Y$ contracting the diagonal $…

math.AG2023

The Fermat cubic and monodromy of lines

Frank Gounelas, Alexis Kouvidakis

In this paper we study properties of the locus of second type lines of a general cubic threefold and fourfold. By analysing the geometry of the Fano scheme of lines of the Fermat c…

math.AG2021★ 4 cited

Geometry of lines on a cubic fourfold

Frank Gounelas, Alexis Kouvidakis

For a general cubic fourfold $X \subset P^{5}$ with Fano scheme of lines $F$ , we prove a number of properties of the universal family of lines $I \to F$ and various subloci. We…

math.AG2020★ 1 cited

On some invariants of cubic fourfolds

Frank Gounelas, Alexis Kouvidakis

For a general cubic fourfold $X \subset P^{5}$ , we compute the Hodge numbers of the locus $S \subset F$ of lines of second type. We also give an upper bound of 6 for the deg…

math.AG2020★ 5 cited

Curves of maximal moduli on K3 surfaces

Xi Chen, Frank Gounelas

We prove that if $X$ is a complex projective K3 surface and $g > 0$ , then there exist infinitely many families of curves of geometric genus $g$ on $X$ with maximal, i.e., $g$ -dimensi…

math.AG2019

Rational curves on lattice-polarised K3 surfaces

Xi Chen, Frank Gounelas, Christian Liedtke

Fix a K3 lattice $Λ$ of rank two and $L \in Λ$ a big and nef divisor that is positive enough. We prove that the generic $Λ$ -polarised K3 surface has an integral nodal rational curve…

math.AG2019

Curves on K3 surfaces

Xi Chen, Frank Gounelas, Christian Liedtke

We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive…

math.AG2019

Cohomology of moduli spaces of Del Pezzo surfaces

Olof Bergvall, Frank Gounelas

We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree three and four as representations of the Weyl group…

math.AG2018★ 7 cited

Remarks on the positivity of the cotangent bundle of a K3 surface

Frank Gounelas, John Christian Ottem

Using recent results of Bayer-Macrì, we compute in many cases the pseudoeffective and nef cones of the projectivised cotangent bundle of a smooth projective K3 surface. We then use…

math.AG2017

Measures of irrationality of the Fano surface of a cubic threefold

Frank Gounelas, Alexis Kouvidakis

For $X$ a smooth cubic threefold we study the Plücker embedding of the Fano surface of lines $S$ of $X$ . We prove that if $X$ is general then the minimal gonality of a covering fam…

math.AG2017

Invariants of Fano varieties in families

Frank Gounelas, Ariyan Javanpeykar

We show that the Picard rank is constant in families of Fano varieties (in arbitrary characteristic) and we moreover investigate the constancy of the index.

math.AG2013

The first cohomology of separably rationally connected varieties

Frank Gounelas

In this short note we prove that if X is a separably rationally connected variety over an algebraically closed field of positive characteristic, then H^1(X, O_X)=0.

math.AG2012

Free Curves on Varieties

Frank Gounelas

We study various generalisations of rationally connected varieties, allowing the connecting curves to be of higher genus. The main focus will be on free curves $f : C \to X$ with larg…