相关论文: On the semistability of instanton sheaves over cer…

We prove that Chern classes in continuous $\ell$-adic cohomology of automorphic bundles associated to representations of $G$ on a projective Shimura variety with data $(G,X)$ are trivial rationally. It is a consequence of Beilinson's…

Let X be an irreducible n-dimensional projective variety in CP^N with arbitrary singular locus. We prove that the L2-(p,1)-d-bar cohomology groups (with respect to the Fubini-Study metric) of the regular part of X are finite dimensional.

Let $\M_{k}^{n}$ be the moduli space of based (anti-self-dual) instantons on $\cpbar$ of charge $k$ and rank $n$. There is a natural inclusion of rank $n$ instantons into rank $n+1$. We show that the direct limit space is homotopy…

Let $E$ be the Whitney sum of complex line bundles over a topological space $X$. Then, the projectivization $P(E)$ of $E$ is called a \emph{projective bundle} over $X$. If $X$ is a non-singular complete toric variety, so is $P(E)$. In this…

We study ACM bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion…

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable…

We construct vector bundles $R^r_\mu$ on a smooth projective curve $X$ having the property that for all sheaves $E$ of slope $\mu$ and rank $r$ on $X$ we have an equivalence: $E$ is a semistable vector bundle $\iff$ $Hom(R^r_\mu,E)=0$. As a…

Let Sigma be a smooth complex curve, and let S be the product ruled surface Sigma \times CP^1. We prove a correspondence conjectured by Donaldson between finite energy U(2)-instantons over the cylinder Sigma \times S^1 \times R, and rank 2…

We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\mathbb{P}^1 \times \mathbb{P}^1$…

The moduli space M_2 of rank four semistable symplectic vector bundles over a curve X of genus two is an irreducible projective variety of dimension ten. Its Picard group is generated by the determinantal line bundle \Xi. The base locus of…

We use a generalization of Horrocks monads for arithmetic Cohen-Macaulay (ACM) varieties to establish a cohomological characterization of linear and Steiner bundles over projective spaces and quadric hypersurfaces. We also study resolutions…

Let $S$ be a very general smooth hypersurface of degree $6$ in $\mathbb{P}^3$. In this paper we will prove that the moduli space of $\mu$-stable rank $2$ torsion free sheaves with respect to hyperplane section having $c_1 =…

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…

To each complex composition algebra $\mathbb{A}$, there associates a projective symmetric manifold $X(\mathbb{A})$ of Picard number one, which is just a smooth hyperplane section of the following varieties ${\rm Lag}(3,6), {\rm Gr}(3,6),…

Generalizing the definitions originally presented by Kuznetsov and Faenzi, we study (possibly non locally free) instanton sheaves of arbitrary rank on Fano threefolds. We classify rank 1 instanton sheaves and describe all curves whose…

Let M be a complex projective manifold with the property that for any compact Riemann surface C and holomorphic map f: C -> M the pullback of the tangent bundle of M is semistable. We prove that in this case M is a curve or a finite etale…

We consider an extension of the instanton bundles definition, given by Casnati-Coskun-Genk-Malaspina, for Fano threefolds, in order to include non locally-free ones on the blow-up $\widetilde{\mathbb{P}^{3}},$ of the projective $3-$space at…

This is a footnote of a recent interesting work of Cohen, Manin and Zagier, where they, among other things, produce a natural isomorphism between the sheaf of (n-1)-th order jets of the n-th tensor power of the tangent bundle of a Riemann…