Related papers: Riemann-Roch for stacky matrix factorizations

This is the integral text of my thesis. The first part is an expanded version of "Riemann-Roch theorems for Deligne-Mumford stacks", where I deal with Artin stacks over general bases. In the second part, I prove some Riemann-Roch statment…

This is the first of a series of papers. Our final goal is to establish Deligne-Riemann-Roch isomorphisms in various settings. In this paper, we establish a uniqueness theorem for Deligne pairings and prove the degree $1$ part of the…

We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…

We deduce the Riemann-Roch type formula expressing the microlocal Euler class of a perfect complex of D-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type…

We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the…

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the…

We give a formula for the Chern character on the DG-category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\mathcal{O}_X)$. Our formula takes values in a Cech model for Hochschild homology. Our…

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their…

In this paper, we prove the functorial Riemann-Roch theorem in positive characteristic for a smooth and projective morphism with any relative dimension. In the case of relative dimension $1$, we have given an analogue with Deligne's…

In the present paper we extend the Riemann-Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and pushforwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann-Roch…

We study the orbifold Hirzebruch-Riemann-Roch (HRR) theorem for quotient Deligne-Mumford stacks, explore its relation with the representation theory of finite groups, and derive a new orbifold HRR formula via an orbifold Mukai pairing. As a…

We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then…

This short note proves a generalization of the Hirzebruch Riemann-Roch theorem equivalent to the Cardy condition described in [1]. This is done using an earlier result [4] that explicitly describes what the Mukai pairing in [1] descends to…

In this article, we construct Chern classes in rational Deligne cohomology for coherent sheaves on a smooth complex compact manifold. We prove that these classes verify the functoriality property under pullbacks, the Whitney formula and the…

This article is part of a series of works by the authors with the goal of completing a far-reaching program propounded by Deligne, aiming to extend the codimension one part of the Grothendieck-Riemann-Roch theorem from isomorphism classes…

Long ago, in math.AG/0112004, we pledged more details on the algebraic version of Chen-Ruan's math.AG/0103156. This is it.

We prove that a Schur function of rectangular shape $(M^n)$ whose variables are specialized to $x_1,x_1^{-1},...,x_n,x_n^{-1}$ factorizes into a product of two odd orthogonal characters of rectangular shape, one of which is evaluated at…

We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our construction is the definition of the…

We prove a Hochschild-Kostant-Rosenberg theorem ("the HKR theorem") which computes the factorization homology of certain smooth commutative ring spectra. In doing so we fix and generalize a THH computation which was first conceived as the…

We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity…