Related papers: On the Segre Invariant for rank two vector bundles…

The problem of studying the two seemingly unrelated sets of invariants forming the Segre and the Verlinde series has gone through multiple different adaptations including a version for the virtual geometries of Quot schemes on surfaces and…

We construct a rank-$2$ indecomposable vector bundle on $\mathbb P^2\times\mathbb P^2$ in characteristic $2$ that does not come from a bundle on $\mathbb P^2$ by factor projection nor from a bundle on $\mathbb P^{m} $ by central projection.…

This is a continuation of "Rational families of vector bundles on curves, I". Let C be a smooth projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1.…

Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this is known to be related to the…

Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential…

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes.

This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…

We use results of M. Aprodu and E. Sernesi to extend a result by Fulton--Harris--Lazarsfeld in Brill--Noether theory of line bundles %and, as well, a result by Aprod-Sernesi in theory of Secant Loci, to Brill--Noether loci of stable bundles…

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…

We consider the problem of constructing matrices of linear forms of constant rank by focusing on the associated vector bundles on projective spaces. Important examples are given by the classical Steiner bundles, as well as some special…

We improve Ottaviani's splitting criterion for vector bundles on a quadric hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and Peterson. Then we give the classification of rank 2 bundles without "inner" cohomology…

We develop strong lower bounds for the span of the projective Stiefel manifolds $X_{n,r}=O(n)/(O(n-r)\times \mathbb Z/2)$, which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves…

A symplectic or orthogonal bundle $V$ of rank $2n$ over a curve has an invariant $t(V)$ which measures the maximal degree of its isotropic subbundles of rank $n$. This invariant $t$ defines stratifications on moduli spaces of symplectic and…

We study the Saito-Ikeda infinitesimal invariant of the ccle defined by curves in their jacobians using rank (k+1) vector bundles and we give a criterion for which the higher cycle class map is not trivial. When k=2, this turns out to be…

We briefly review an open conjecture about Higgs bundles that are semistable with after pulling back to any curve, and prove it in the rank 2 case. We also prove a set of inequalities holding for H-nef Higgs bundles that generalize some of…

Let $k$ be an algebraically closed field with characteristic $2$, and let $X$ be a smooth projective algebraic curve of genus $g \geqslant 2$ over $k$. Let $\mathcal{M}^s_X(2,\mathcal{L})$ be the moduli space of rank $2$ stable vector…

We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or…

This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney…

Several families of rank-two vector bundles on Hirzebruch surfaces are shown to consist of all very ample, uniform bundles. Under suitable numerical assumptions, the projectivization of these bundles, embedded by their tautological line…

In this work we deal with vector bundles of rank two on a Fano manifold $X$ with $b_2=b_4=1$. We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the…