Related papers: Universal vector bundle over the reals

This article is concerned with the convexity properties of universal covers of projective varieties. We study the relation between the convexity properties of the universal cover of X and the properties of the pullback map sending vector…

In this paper, we investigate the existence of Ulrich bundles on a smooth complete intersection of two $4$-dimensional quadrics in $\mathbb P^5$ by two completely different methods. First, we find good ACM curves and use Serre…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…

Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute the…

Let $X$ be a projective K3 surfaces. In two examples where there exists a fine moduli space $M$ of stable vector bundles on $X$, isomorphic to a Hilbert scheme of points, we prove that the universal family $\mathcal{E}$ on $X\times M$ can…

We combine the idea of Chang and Ran [Invent. Math. 76 (1984), 41-54] of using monads of vector bundles on the projective 3-space to prove the unirationality of the moduli spaces of curves of low genus with our classification of globally…

Let Y be a subvariety of a smooth projective variety X, and V a vector bundle on X. Given that the restriction of V to Y splits into a direct sum of line bundles, we ask whether V splits on X. I answer this question in affirmative if holds:…

We study varieties $X \subseteq \mathbb P^N$ of dimension $n$ such that $T_X(k)$ is an Ulrich vector bundle for some $k \in \mathbb Z$. First we give a sharp bound for $k$ in the case of curves. Then we show that $k \le n+1$ if $2 \le n \le…

Let $(X,H)$ be a polarized K3 surface with $\mathrm{Pic}(X) = \mathbb Z H$, and let $C\in |H|$ be a smooth curve of genus $g$. We give an upper bound on the dimension of global sections of a semistable vector bundle on $C$. This allows us…

We prove that on a general hypersurface in $\mathbb{P}^N$ of degree $d$ and dimension at least $2$, if an arithmetically Cohen-Macaulay (ACM) bundle $E$ and its dual have small regularity, then any non-trivial Hodge class in $H^{n}(X,…

The moduli space M(r,d) of stable, rank r, degree d vector bundles on a smooth projective curve of genus g>1 is shown to be birational to M(h,0) x A, where h=hcf(r,d) and A is affine space of dimension (r^2-h^2)(g-1). The birational…

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this…

Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_X-coherent D_X-modules) on X without relying on…

Let C be a projective smooth curve of genus g> 1. Let E be a vector bundle of rank r on C. For each integer r'<r, associate to E the invariant s_{r'}(E)=r'deg(E)-rdeg(E') where E'is a subbundle of E of rank r' and maximal degree. For every…

Let n > 2 and let d < (n+1)/2. We prove that for a general hypersurface X of degree d in P^n, all the genus 0 Kontsevich moduli spaces M_{0,n}(X,e) are irreducible, reduced, local complete intersection stacks of the expected dimension.

Let $Y$ be a normal and projective variety over an algebraically closed field $k$ and $V$ a vector bundle over $Y$. We prove that if there exist a $k$-scheme $X$ and a finite surjective morphism $g:X\to Y$ that trivializes $V$ then $V$ is…

We investigate on the existence of some "sporadic", rank-$r \geqslant 1$ Ulrich vector bundles on suitable $3$-fold scrolls $X$ over the Hirzebruch surface $\mathbb{F}_0$, which arise as tautological embeddings of projectivization of…

Let X be a smooth complex irreducible projective variety of dimension $n \geq 2$ and $H$ be an ample line bundle on $X$. In this paper, we construct families of $\mu_H$-stable vector bundles on $X$ having fixed determinant and rank $r$,…

We prove that the modular component $\mathcal M(r)$, constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank $r$ and given Chern classes,…

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally…