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We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Blochs conjecture on Chern classes of flat vector bundles on smooth complex projective varities but in some cases they give a more precise information. We also study Higgs version of Blochs conjecture and analogous problems in the positive characteristic case.
We construct many``low rank algebraic vector bundles on ``simple smooth affine varieties of high dimension. In a related direction, we study the existence of polynomial representatives of elements in the classical (unstable) homotopy groups of sphere
We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2le dleq n-d)$ to be the Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where $k$ is an a
We consider a uniform $r$-bundle $E$ on a complex rational homogeneous space $X$ %over complex number field $mathbb{C}$ and show that if $E$ is poly-uniform with respect to all the special families of lines and the rank $r$ is less than or equal to
We construct smooth rational real algebraic varieties of every dimension $ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.
This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.