Related papers: The Newstead-Ramanan conjecture for Chern classes

Let $E$ be a vector bundle of rank $r\geq 2$ on a smooth projective curve $C$ of genus $g \geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\le k\le r-1$ we define $${\se}_k(E):=k\deg…

We show that the cohomological Brauer groups of the moduli stacks of stable genus $g$ curves over the integers and an algebraic closure of the rational numbers vanish for any $g\geq 2$. For the $n$ marked version, we show the same vanishing…

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…

We compute some Gromov-Witten invariants of the moduli space of odd degree rank two stable vector bundles over a Riemann surface of any genus. Next we find the first correction term for the quantum product of this moduli space and hence get…

We discuss stability conditions for all rank-2 ample vector bundles on Hirzebruch surfaces with the second Chern class less than 7.

In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an…

Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…

In this paper we investigate the moduli spaces of semistable coherent sheaves of rank two on the projective space $\mathbb{P}^3$ and the following rational Fano manifolds of the main series - the three-dimensional quadric $X_2$, the…

In this paper we study ACM vector bundles $\E$ of rank $k \geq 3$ on hypersurfaces $X_r \subset\Pj^4$ of degree $r \geq 1$. We consider here mainly the case of degree $r = 4$, which is the first unknown case in literature. Under some…

This paper studies spaces of generalized theta functions for odd orthogonal bundles with nontrivial Stiefel-Whitney class and the associated space of twisted spin bundles. In particular, we prove a Verlinde type formula and a dimension…

We show that the moduli space of $A$-line bundles with minimal second Chern class is a fine moduli space, where $A$ is a maximal quaternion order on $\mathbb{P}^{2}$ ramified along a smooth quartic. We prove that there is a fully faithful…

Let X be a Hermitian locally symmetric space. We prove that every Chern class of X has a canonical lift to the cohomology of the Baily- Borel-Satake compactification X* of X and that the resulting Chern numbers satisfy the Hirzebruch…

Kawamata proposed a conjecture predicting that every nef and big line bundle on a smooth projective variety with trivial first Chern class has nontrivial global sections. We verify this conjecture for several cases, including (i) all…

In this note, we investigate the Chern classes of flat bundles in the arithmetic Deligne Cohomology, introduced by Green-Griffiths, Asakura-Saito. We show nontriviality of the Chern classes in some cases and the proof also indicates that…

This paper establishes the correctness of a conjecture of Bertram-Feinberg and Mukai for a special class of globally generated rank-two bundles with canonical determinant over a generic Riemann surface of genus at least four.

The crystalline Chern classes of the value of a locally free crystal vanish on a smooth variety defined over a perfect field. Out of this we conclude new cases of de Jong's conjecture relating the geometric \'etale fundamental group of a…

Let $C$ be an algebraic curve of genus $g \geq 2$ and $M_L$ be the moduli space of rank 2 stable vector bundles on $C$ whose determinants are isomorphic to a fixed line bundle $L$ of degree 1 on $C.$ S. del Bano studied motives of moduli…

Associated to a symmetrisable Cartan matrix $C$, Geiss-Lerclerc-Schr\"{o}er constructed and studied a class of Iwanaga-Gorenstein algebras $H$. They proved a generalised version of Gabriel's Theorem, that is, the rank vectors of…

Given a vector bundle, its (stable) order is the smallest positive integer n such that the n-fold self-Whitney sum is (stably) trivial. So far, the order and the stable order of the canonical vector bun- dle over configuration spaces of…

In this article we prove a general result on a nef vector bundle $E$ on a projective manifold $X$ of dimension $n$ depending on the vector space $H^{n,n} (X, E). $ It is also shown that $H^{n,n} (X, E)=0$ for an indecomposable nef rank 2…