Related papers: Dalian notes on rational Pontryagin classes

In this paper, we study rational sections of the relative Picard scheme of a linear system on a smooth projective variety. We prove that if the linear system is basepoint-free and the locus of non-integral divisors has codimension at least…

In this article we show that there are at most two integers up to $2(n-k)$, which can occur as the degrees of nonzero Stiefel-Whitney classes of vector bundles over the Stiefel manifold $V_k(\mathbb{R}^n)$. In the case when $n> k(k+4)/4$,…

The aim of this note is to construct sequences of vector bundles with unbounded rank and discriminant on an arbitrary algebraic surface. This problem, on principally polarized abelian varieties with cyclic Neron-Severi group generated by…

We show that for any ample line bundle on a smooth complex projective variety with nonnegative Kodaira dimension, the semistability of co-Higgs bundles of implies the semistability of bundles. Then we investigate the criterion for surface…

We construct families of non-trivial universal rigid secondary classes for foliations, and then discuss their application to prove that foliations are not homotopic. An observation of Lawson about the non-triviality of the normal Pontrjagin…

We prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S^n x S^n, in the…

We show that surface bundles over surfaces with base and fiber of genus at least 2 have non-vanishing simplicial volume.

The cohomology ring of the moduli space of stable holomorphic vector bundles of rank n and degree d over a Riemann surface of genus g>1 has a standard set of generators when n and d are coprime. When n=2 the relations between these…

We show that instanton bundles of rank $r\le 2n-1$, defined as the cohomology of certain linear monads, on an $n$-dimensional projective variety with cyclic Picard group are semistable in the sense of Mumford-Takemoto. Furthermore, we show…

For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism…

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…

We present natural families of coordinate algebras of noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an R-matrix which is involutive and satisfies the Yang-Baxter equations. As a…

In this paper we point out the natural relation between $\mathbb Q$-twisted objects of the derived category of abelian varieties, cohomological rank functions, and semihomogeneous vector bundles. We apply this to two basic classes of…

Let $E$ be an indecomposable rank two vector bundle on the projective space $\PP^n, n \ge 3$, over an algebraically closed field of characteristic zero. It is well known that $E$ is arithmetically Buchsbaum if and only if $n=3$ and $E$ is a…

We introduce $\varepsilon$-approximate versions of the notion of Euclidean vector bundle for $\varepsilon \geq 0$, which recover the classical notion of Euclidean vector bundle when $\varepsilon = 0$. In particular, we study \v{C}ech…

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli…

The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…

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.…

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…

We study the topology of the 13 dimensional positively curved Bazaikin spaces. We show that there is only one such manifold which is homotopy equivalent to a homogeneous space, the so called Berger space. This is in contrast to the case of…