7 papers
On the algebraic structure of differentially homogeneous polynomials
Antoine Etesse
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra,…
On the Schmidt--Kolchin conjecture on differentially homogeneous polynomials. Applications to (twisted) jet differentials on projective spaces
Antoine Etesse
The main goal of this paper is to prove the Schmidt--Kolchin conjecture. This conjecture says the following: the vector space of degree \(d\) differentially homogeneous polynomials…
Cohomology of twisted symmetric powers of cotangent bundles of smooth complete intersections
Antoine Etesse
In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular t…
Geometric generalized Wronskians. Applications in intermediate hyperbolicity and foliation theory
Antoine Etesse
In this paper, we introduce a sub-family of the usual generalized Wronskians, that we call geometric generalized Wronskians. It is well-known that one can test linear dependance of…
Algebraic intermediate hyperbolicities
Antoine Etesse, Ariyan Javanpeykar, Erwan Rousseau
We extend Lang's conjectures to the setting of intermediate hyperbolicity and prove two new results motivated by these conjectures. More precisely, we first extend the notion of al…
Complex-analytic intermediate hyperbolicity, and finiteness properties
Antoine Etesse
Motivated by the finiteness of the set of automorphisms Aut(X) of a projective manifold X, and by Kobayashi-Ochiai's conjecture that a projective manifold dim(X)-analytically hyper…
Ampleness of Schur powers of cotangent bundles and k-hyperbolicity
Antoine Etesse
In this paper, we study a variation of a conjecture of Debarre on positivity of cotangent bundles of complete intersections. We establish the ampleness of Schur powers of cotangent…