相关论文: Chern character of Schur bundles

Let ${\mathsf F}$ be the Schur functor from the category of finite dimensional ${\mathcal H}_{\vartriangle}(r)_\mathbb C$-modules to the category of finite dimensional ${\mathcal S}_{\vartriangle}(n,r)_{\mathbb{C}}$-modules, where…

Given a matrix factorization, we use the Atiyah class to give an algebraic Chern-Weil type construction to its Chern character; this allows us to realize the Chern character in an explicit way. It also generalizes the existing result to any…

Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the…

We prove an explicit formula for the truncated Atiyah class of a bounded complex of vector bundles. Furthermore, we show that the first truncated Chern class of such a complex only depends on its determinant.

This paper surveys topological results obtained from characteristic classes built from the two types of traces on the algebra of pseudodifferential operators of nonpositive order. The main results are the construction of a universal $\hat…

Let $X$ be a $d$ dimensional projective manifold, $E$ be an ample vector bundle on $X$ and $0\le \lambda_N\le \lambda_{N-1} \le \cdots \le \lambda_1 \le \operatorname{rank}(E)$ be a partition of $d-2$. We prove that the Schur class…

We introduce a new family of tautological relations of the moduli space of stable curves of genus $g$. These relations are obtained by computing the Poincar\'e-dual class of empty loci in the Hodge bundle. We use these relations to obtain a…

For any complex vector bundle $E^k$ of rank $k$ over a manifold $M^m$ with Chern classes $c_i \in H^{2i}(M^m,\Z)$ and any non-negative integers $l_1, >..., l_k$ we show the existence of a positive number $N(k,m)$ and the existence of a…

We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as…

Let $E$ be a vector bundle of rank $n$ on $\mathbb{P}^1$. Fix a positive integer $d$. Let $\mathcal{Q}(E,d)$ denote the Quot scheme of torsion quotients of $E$ of degree $d$ and let $Gr(E,d)$ denote the Grassmann bundle that parametrizes…

A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler…

Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we construct smooth affine algebras $B$ over ${\mathbb F}_0$, with $\dim B=p+2$. Further, we construct…

We prove that a vector bundle $\pi : E \to M$ is characterized by the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of…

We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses…

We study singular hermitian metrics on holomorphic vector bundles, following Berndtsson-P{\u{a}}un. Previous work by Raufi has shown that for such metrics, it is in general not possible to define the curvature as a current with measure…

We study locally free sheaves of rank two on the projective line over the integers, especially indecomposable ones. Subsequently we apply various concepts of Arakelov geometry to these sheaves. We compute for example the arithmetic Chern…

Given a supervector bundle $E = E_0\oplus E_1 \to M$, we exhibit a parametrization of Quillen superconnections on $E$ by graded connections on the Cartan-Koszul supermanifold $(M;\Omega (M))$. The relation between the curvatures of both…

A residue formula is given for the Verlinde formula, which allows one to calculate its coefficients as a polynomial in the level and connects it to the Riemann-Roch formula on the moduli space of vector bundles on a curve.

We prove that the Lie algebra $\mathcal{S}(\mathcal{P}(E,M))$ of symbols of linear operators acting on smooth sections of a vector bundle $E\to M,$ characterizes it. To obtain this, we assume that $\mathcal{S}(\mathcal{P}(E,M))$ is seen as…

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…