Related papers: On Serrano's conjecture on Projective bundles

Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz spaces in algebraic geometry, we investigate the vector…

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an…

In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…

We study the positivity properties of the projectivization of a parabolic bundle over a smooth complex projective curve. The generators of its N\'eron--Severi group are computed, and the positive cone is determined. In particular, we…

The aim of this note is to introduce a stable version of Terao conjecture, using the notion of infinitely stably extendability of vector bundles on $\mathbb P^n$, considered and characterized by I. Coanda in arXiv:0907.4040.

Let $X$ be a complex smooth projective variety such that the exterior power of the tangent bundle $\bigwedge^{r} T_X$ is nef for some $1\leq r<\dim X$. We prove that, up to an \'etale cover, $X$ is a Fano fiber space over an Abelian…

We introduce and motivate the following question: Is every effective strictly nef Cartier divisor on a projective variety big? In the appendix, Andreas H\"oring produces a counterexample, thus providing a negative answer.

A long standing conjecture, known to us as the Eisenbud Goto conjecture, states that an n-dimensional variety embedded with degree $d$ in the $N$- dimensional projective space is $(d-(N-n)+1)$-regular in the sense of Castelnuovo-Mumford. In…

In this paper we consider the singularities of the varieties parameterizing stable vector bundles of fixed rank and degree with sections on a smooth curve of genus at least two. In particular, we extend results of Y. Laszlo, and of the…

In this article, we investigate the instability of syzygy bundles corresponding to globally generated vector bundles on smooth irreducible projective surfaces under change of polarization.

In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a…

Given a bundle gerbe on a compact smooth manifold or, more generally, on a compact \'etale Lie groupoid $M$, we show that the corresponding category of gerbe modules, if it is non-trivial, is equivalent to the category of finitely generated…

Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…

We study stable rank 2 vector bundles with trivial determinant whose Frobenius pull back is non stable over a general curve of genus g>1. In genus 2, we apply recent results about the theta divisor associated to the bundle B of locally…

In this note we give a complete description of all the hyperplane section of the projective bundle associated to the tangent bundle of $\mathbb{P}^2$ under its natural embedding in $\mathbb{P}^7.$ As an application one obtains a description…

The purpose of this short note is to give a remark on the decomposition theorem for direct images of canonical sheaves tensorized with Nakano semipositive vector bundles. Although our result is a direct consequence of Takegoshi's work, it…

We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering…

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed…

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^3$. We use this fact, together with the pure spinor superfield formalism, to study…

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…