Related papers: Some topological properties of surface bundles

Given integers $a_1,a_2,a_3$, there is a complex rank $3$ topological bundle on $\mathbb CP^5$ with $i$-th Chern class equal to $a_i$ if and only if $a_1,a_2,a_3$ satisfy the Schwarzenberger condition. Provided that the Schwarzenberger…

A gauge group is the topological group of automorphisms of a principal bundle. We compute the integral cohomology ring of the classifying spaces of gauge groups of principal U(n)-bundles over the 2-sphere by generalizing the operation for…

Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all noncommutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The…

Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental…

We describe the singular cohomology ring, the K-ring of complex vector bundles, the Chow ring, and the Grothendieck ring of coherent sheaves of the total space of the fibre bundle with base space an irreducible nonsingular complete…

Here we consider the product of varieties with $n$-blocks collections . We give some cohomological splitting conditions for rank 2 bundles. A cohomological characterization for vector bundles is also provided. The tools are Beilinson's type…

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is…

Every surface bundle with genus $g$ fiber has a canonical Heegaard splitting of genus $2g+1$. We classify the mapping class groups of such Heegaard splittings in the case when the surface bundle has a sufficiently complicated monodromy map.

For any closed oriented surface F of genus at least three, we prove the existence of foliated F-bundles over surfaces such that the signatures of the total spaces are non-zero. We can arrange that the total holonomy of the horizontal…

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…

We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of…

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a…

A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…

We give a construction of the second Chern number of a vector bundle over a smooth projective surface by means of adelic transition matrices for the vector bundle. The construction does not use an algebraic $K$-theory and depends on the…

We exhaustively classify topological equivariant complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most)…

We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Afterwards we use the bounded rational sections of a…

Assuming Hartshorne's conjecture on complete intersections, we classify projective bundles over projective spaces which has a smooth blow up structure over another projective space. Under some assumptions, we also classify projective…

We prove that a general determinantal hypersurface of dimension 3 is nodal. Moreover, in terms of Chern classes associated with bundle morphisms, we derive a formula for the intersection homology Euler characteristic of a general…