Related papers: On the nonexistence of certain morphisms from Gras…

We look at the following question raised by Koll\'ar and Peskine. (Actually, it is a slightly weaker version of their question.) Let $V_t$ be a family of rank two vector bundles on $\Bbb P^3$. Assume that the general member of the family is…

Let X be a subvariety of $P^n$ defined by equations of degrees $ d =(d_1,...,d_s)$, over an algebraically closed field k of any characteristic. We study properties of the Fano scheme $F_r(X)$ that parametrizes linear subspaces of dimension…

We study the rank stratification for the differential of a Lagrangian fibration over a smooth basis. We also introduce and study the notion of Lagrangian morphism of vector bundles. As a consequence, we prove some of the vanishing, in the…

A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…

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…

We develop a theory of ``ad hoc'' Chern characters for twisted matrix factorizations associated to a scheme $X$, a line bundle ${\mathcal L}$, and a regular global section $W \in \Gamma(X, {\mathcal L})$. As an application, we establish the…

We calculate the Chern classes and Chern numbers for the natural almost Hermitian structures of the partial flag manifolds F_n=SU(n+2)/S(U(n)\times U(1)\times U(1)). For all n>1 there are two invariant complex algebraic structures, which…

We prove an analogue of the Lefschetz (1,1) Theorem characterizing cohomology classes of Cartier divisors (or equivalently first Chern classes of line bundles) in the second integral cohomology. Let $X$ be a normal complex projective…

In this {paper}, we consider holomorphic embeddings of $Gr(2,m)$ into $Gr(2,n)$. We study such embeddings by finding all possible total Chern classes of the pull-back of the universal bundles under these embeddings. Using the relations…

We prove some strong results on approximation of strongly semistable bundles with vanishing numerical Chern classes by filtrations, whose quotients are line bundles of similar slope. This generalizes some earlier results of…

Let $X$ be a smooth projective variety over a perfect field $k$ of characteristic $p>0$, and $V$ be a vector bundle over $X$. It is well known that if $X$ is a curve and $V$ is not strongly semistable, then some Frobenius pullback…

We construct Chern-Weil classes on infinite dimensional vector bundles with structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive order classical pseudo-differential operators acting on a finite rank vector bundle $E$…

Let G be a complex connected reductive group. The representation ring R(G) admits a canonical filtration defined in terms of the lambda-structure. We compute the associated graded ring gr R(G) (over Q) and the Chern classes of a…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

For a finite dimensional vector space V of dimension n, we consider the incidence correspondence (or partial flag variety) X in P(V) x P(V*), parametrizing pairs consisting of a point and a hyperplane containing it. We completely…

This work revolves around the question of whether a given resonance variety is associated with a vector bundle. We show the existence of a family of natural morphisms on a stratification of the resonance variety to a suitable family of a…

We study fractional quantum Hall states with quasihole excitations, on Riemann surfaces of arbitrary genus. For configurations with $m$ quasiholes we construct a vector bundle above the $m$-th symmetric power of the curve so that the fiber…

CORRECTION. One of the main results in this paper contains a fatal error. We cannot conclude the existence of nontrivial vector bundles on X from the nontriviality of its K-group. The K-group that is computed here is the Grothendieck group…

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…

Alan Weinstein showed that certain characteristic numbers of any Riemannian submersion with totally geodesic fibers and positive vertizontal curvatures are nonzero. In this paper we explicitly compute these invariants in terms of Chern and…