Related papers: Hilbert irreducibility for varieties with a nef ta…

We show that a nef line bundle on a proper scheme over an excellent base is semiample if and only if it is semiample after restricting to characteristic zero and to positive characteristic. In the process of the proof, we provide a…

In this paper, we prove the Bogomolov-Gieseker type inequality conjecture for threefolds with nef tangent bundles. As a corollary, there exist Bridgeland stability conditions on these threefolds.

We prove the Shafarevich conjecture for varieties with globally generated cotangent bundle, subject to mild numerical conditions.

We prove that smooth Fano 5-folds with nef tangent bundles and Picard numbers greater than one are rational homogeneous manifolds.

As in our previous work [1] we address the problem to determine the splitting of the normal bundle of rational curves. With apolarity theory we are able to characterize some particular subvarieties in some Hilbert scheme of rational curves,…

In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle…

This paper studies the Ulrich property of homogeneous vector bundles on rational homogenous varieties. We provide a criterion for an initialized irreducible homogeneous vector bundle on a rational homogeneous variety with any Picard number…

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny…

Let $S$ be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in $\mathbb{P}^s$. We prove that, under certain positivity conditions, its Hilbert square $\mathrm{Hilb}^2(S)$ is…

We examine the relationship between nonabelian Hodge theory for Riemann surfaces and the theory of vector valued modular forms. In particular, we explain how one might use this relationship to prove a conjectural three-term inequality on…

A rational Lagrangian fibration f on an irreducible symplecitc variety V is a rational map which is birationally equivalent to a regular surjective morphism with Lagrangian fibers. By analogy with K3 surfaces, it is natural to expect that a…

This paper gives a classification of the topology of vector fields which are nowhere tangent to the fibers of a Seifert fibering.

In this article we prove the irreducibility of the Hilbert scheme of rationnal curves on homogeneous varieties with fixed class in the Chow ring. This result has also been proved by J. F. Thomsen [T] and B. Kim and R. Pandharipande [KP].…

We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.

We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its dependence on external arithmetic conjectures, we render the…

The weak Hilbert property (WHP) for varieties over fields of characteristic zero was introduced by Corvaja and Zannier in 2017. There exist integral variants of WHP for arithmetic schemes. We present new fibration theorems for both the WHP…

Let X be the quasi-projective symplectic surface that is given by the total space of the invertible sheaf O(-2) over the projective line. Let Hilb X be the family of Hilbert schemes of points on X. We give and prove a closed formula…

We prove vanishing results for the generalized Miller-Morita-Mumford classes of some smooth bundles whose fiber is a closed manifold that supports a nonpositively curved Riemannian metric. We also find, under some extra conditions, that the…

We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety $V$ in terms of the geometric degree of $V$. We first analyze the case of curves, showing an explicit relation…

The aim of the present paper is to investigate new classes of symplectically fat fibre bundles. We prove a general existence theorem for fat vectors with respect to the canonical invariant connections. Based on this result we give new…