Do you want to publish a course? Click here

On algebraic Chern classes of flat vector bundles

70   0   0.0 ( 0 )
 Added by Adrian Langer
 Publication date 2021
  fields
and research's language is English
 Authors Adrian Langer




Ask ChatGPT about the research

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.



rate research

Read More

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 spheres. Using techniques of A^1-homotopy theory, we are able to produce ``motivic lifts of elements in classical homotopy groups of spheres; these lifts provide interesting polynomial maps of spheres and algebraic vector bundles.
368 - Rong Du , Xinyi Fang , Yun Gao 2019
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 algebraically closed field of characteristic $p>0$. Let $E$ be a uniform vector bundle over $G$ of rank $rle d$. We show that $E$ is either a direct sum of line bundles or a twist of a pull back of the universal bundle $H_d$ or its dual $H_d^{vee}$ by a series of absolute Frobenius maps. In the second part, splitting properties of vector bundles on general flag varieties $F(d_1,cdots,d_s)$ in characteristic zero are considered. We prove a structure theorem for bundles over flag varieties which are uniform with respect to the $i$-th component of the manifold of lines in $F(d_1,cdots,d_s)$. Furthermore, we generalize the Grauert-M$ddot{text{u}}$lich-Barth theorem to flag varieties. As a corollary, we show that any strongly uniform $i$-semistable $(1le ile n-1)$ bundle over the complete flag variety splits as a direct sum of special line bundles.
168 - Rong Du , Xinyi Fang , Yun Gao 2020
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 some number that depends only on $X$, then $E$ is either a direct sum of line bundles or $delta_i$-unstable for some $delta_i$. So we partially answer a problem posted by Mu~{n}oz-Occhetta-Sol{a} Conde. In particular, if $X$ is a generalized Grassmannian $mathcal{G}$ and the rank $r$ is less than or equal to some number that depends only on $X$, then $E$ splits as a direct sum of line bundles. We improve the main theorem of Mu~{n}oz-Occhetta-Sol{a} Conde when $X$ is a generalized Grassmannian by considering the Chow rings. Moreover, by calculating the relative tangent bundles between two rational homogeneous spaces, we give explicit bounds for the generalized Grauert-M{u}lich-Barth theorem on rational homogeneous spaces.
116 - Adrien Dubouloz 2018
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.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا