Related papers: Superconnection and Orbifold Chern character
In this paper, we study the Chern character operators on the equivariant cohomology of the Hilbert schemes of points in the complex affine plane $C^2$ with the action of the torus $(C^*)^2$, and partially verify Okounkov's Conjecture [Oko,…
In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $$ W_r=\{(x,y,z,t)|xy-z^{2r}+t^2=0 \}/\mu_r(a,-a,1,0), r\geq 1, $$ which we call orbi-conifolds. The related orbifold symplectic conifold…
Chern plethysm (introduced by Billey, Rhoades, and Tewari) is a geometric way to produce Schur positive symmetric polynomials. We present combinatorial interpretations for the Schur expansions of special cases of Chern plethysm. We also…
Supercurrents, as introduced by Lagerberg, were mainly motivated as a way to study tropical varieties. Here we will associate a supercurrent to any smooth submanifold of $\R^n$. Positive supercurrents resemble positive currents in complex…
Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. Solving the equation, one will obtain, in each Bott--Chern cohomology class, a…
The so-called multilayer wave functions were introduced in the study of the fractional Quantum Hall effect by Halperin and others. They are defined with the help of a symmetric matrix $K$ in $M^k(\mathbb{N})$, which encodes the couplings…
From 1980s, it is an open problem of proposing cohomologic formula for the basic index of a transversally elliptic basic differential operator on a vector bundle over a foliated manifold. In 1990s, El Kacimi-Alaoui has proprosed to use the…
In this paper we introduce the Cheeger-Simons cohomology of a global quotient orbifold. We prove that the Cheeger-Simons cohomology of the orbifold is isomorphic to its Beilinson-Deligne cohomology. Furthermore we construct a string…
We define the superclasses for a classical finite unipotent group $U$ of type $B_{n}(q)$, $C_{n}(q)$, or $D_{n}(q)$, and show that, together with the supercharacters defined in a previous paper, they form a supercharacter theory. In…
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommutative super surfaces are introduced and it is shown that the…
We show that the characteristic polynomial of a hyperplane arrangement can be recovered from the class in the Grothendieck group of varieties of the complement of the arrangement. This gives a quick proof of a theorem of Orlik and Solomon…
In this paper I present a new and unified method of proving character formulas for discrete series representations of connected Lie groups by applying a Chern character-type construction to the matrix factorizations of [FT] and [FHT3]. In…
In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we…
In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for To\"en and Vezzosi's secondary Chern character. As a main application, we establish…
Given a compact Chern-Ricci flat balanced orbifold, we show that its blow-up at a finite family of smooth points admits constant Chern scalar curvature balanced metrics, extending Arezzo-Pacard's construction to the balanced setting.…
We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients…
We study intersection cohomology of character varieties for punctured Riemann surfaces with prescribed monodromies around the punctures. Relying on previous result from Mellit for semisimple monodromies we compute the intersection…
We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…
The existence of bivariant Chern classes was conjectured by W.Fulton and R.MacPherson and proved by J.P.Brasselet for cellular morphisms of analytic varieties. In this paper we show that restricted to morphisms whose target varieties are…
The Chern character maps are one of the most important working tools in mathematics. Although they admit numerous different constructions, they are not yet fully understood at the conceptual level. In this note we eliminate this gap by…