Related papers: On algebraic Chern classes of flat vector bundles

Let $A$ be an Azumaya algebra over a field. If $G$ is the group of automorphisms of $A$ and $X$ denotes a projective homogeneous variety under $G$, we construct in a very explicit way and under suitable hypotheses a bundle $\mathcal{V}$ on…

Using compactifications in the logarithmic cotangent bundle, we obtain a formula for the Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement. This generalizes earlier results of…

We propose a version of the Hodge conjecture in Bott-Chern cohomology and using results from characterizing real holomorphic chains by real rectifiable currents to provide a proof for this question. We define a Bott-Chern differential…

Using raising operators and geometric arguments, we establish formulas for the K-theory classes of degeneracy loci in classical types. We also find new determinantal and Pfaffian expressions for classical cases considered by Giambelli: the…

We study the p-adic deformation properties of algebraic cycle classes modulo rational equivalence. We show that the crystalline Chern character of a vector bundle lies in a certain part of the Hodge filtration if and only if, rationally,…

We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification…

We obtain examples of smooth projective varieties over $\mathbb{C}$ that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number…

We develop a framework for describing vector bundles on $\mu_n$-gerbes over curves and illustrate the construction through two detailed examples. Using the interpretation of Brauer classes as obstructions to descending determinantal line…

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…

We describe two constructions giving rise to curved $A_{\infty}$-algebras. The first consists of deforming $A_{\infty}$-algebras, while the second involves transferring curved dg structures that are deformations of (ordinary) dg structures…

We review the Kohno-Drinfeld theorem as well as a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection D on the Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the root hyperplanes…

We study the Chow group of 1-cycles of the moduli space of semistable parabolic vector bundles of fixed rank, determinant and a generic weight over a nonsingular projective curve over $\mathbb{C}$ of genus at least 3. We show that, the Chow…

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 develop a theory of arithmetic characteristic classes of (fully decomposed) automorphic vector bundles equipped with an invariant hermitian metric. These characteristic classes have values in an arithmetic Chow ring constructed by means…

We classify nef vector bundles on a smooth hyperquadric of dimension $\geq 4$ with first Chern class two over an algebraically closed field of characteristic zero.

We show that a flat principal bundle with compact connected structure group and its adjoint bundles of Lie groups have the same cohomology as the trivial bundle, which is done by proving they satisfy the condition for the Leray-Hirsch…

We provide a formula for the Chern character of a holomorphic vector bundle in the hyper-cohomology of the de Rham complex of holomorphic sheaves on a complex manifold. This Chern character can be thought of as a completion of the Chern…

Complex Chern-Simons bundles are line bundles with connection, originating in the study of quantization of moduli spaces of flat connections with complex gauge groups. In this paper we introduce and study these bundles in the families…

In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete…

A result of A. King and C. Walter asserts that the Chow ring of a fine quiver moduli space is generated by the Chern classes of universal bundles if the quiver is acyclic. We will show that defining relations between these Chern classes…