相关论文: Chern Classes of Toric Variety Bundles

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…

In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the…

The notion of a tropical vector bundle on a toric variety was recently introduced by Khan-Maclagan and Kaveh-Manon. In this paper, we study the Euler characteristic and rank of global sections for tropical vector bundles. We associate a…

The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for…

We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study equivariant versions of Todd, Chern and…

We give a short proof of the Zariski-Lipman conjecture for toric varieties: any complex toric variety with locally free tangent sheaf is smooth.

We provide formulas for the Chern classes of linear submanifolds of the moduli spaces of Abelian differentials and hence for their Euler characteristic. This includes as special case the moduli spaces of k-differentials, for which we set up…

Given a flexible $n$-gon with generic side lengths, the moduli space of its configurations in $\mathbb{R}^2$ as well as in $\mathbb{R}^3$ is a smooth manifold. It is equipped with $n$ \textit{tautological} line bundles whose definition is…

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 show that the Virasoro conjecture in Gromov--Witten theory holds for the the total space of a toric bundle $E \to B$ if and only if it holds for the base $B$. The main steps are: (i) we establish a localization formula that expresses…

We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex 4-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over…

In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are…

The goal of this paper is to construct universal cohomology classes on the moduli space of stable bundles over a curve when it is not a fine moduli space, i.e. when the rank and degree are not coprime. More precisely, we show that certain…

The Hirzebruch $td_y(X)$ class of a complex manifold X is a formal combination of Chern characters of the sheaves of differential forms multiplied by the Todd class. The related $\chi_y$-genus admits a generalization for singular complex…

We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme $X$ over an idempotent…

Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to…

We begin by explaining how a physical problem of studying the quantum Hall effect on a closed surface $C$ leads, via Laughlin's approach, to a mathematical question of describing the rank and the first Chern class of a particular vector…

The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work "Chern character, loop spaces and derived algebraic geometry". For this, we introduce and…

Here we consider higher Chern classes of vector bundles of conformal blocks on $\overline{\operatorname{M}}_{0,n}$, giving explicit formulas for them, and extending various results that hold for first Chern classes to them. We use these…

Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite…