Related papers: Equivariant Elliptic Genera and Local McKay Corres…

In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and…

We show that for smooth complex projective varieties the most general combinations of chern numbers that are invariant under the K-equivalence relation consist of the complex elliptic genera. Combined with a recent result of Totaro, we…

We compute Gromov-Witten (GW) and Donaldson-Thomas (DT) invariants (and also descendant invariants) for local CY 4-folds over Fano 3-folds, V_5 and V_22 up to degree 3. We use torus localization for GW invariants computation, and use…

We compute, by two methods, the genus one degree zero orbifold Gromov-Witten invariants with non-stacky insertions which are exceptional cases of the dilaton and divisor equations. One method involves a detailed analysis of the relevant…

The paper contains a proof that elliptic genus of a Calabi-Yau manifold is a Jacobi form, finds in which dimensions the elliptic genus is determined by the Hodge numbers and shows that elliptic genera of a Calabi-Yau hypersurface in a toric…

The elliptic quasimap potential function is explicitly calculated for Calabi-Yau complete intersections in projective spaces by Kim and Lho. We extend this result to local Calabi-Yau varieties. Using this as well as the wall crossing…

We establish Green equivalences for all Mackey 2-functors, without assuming Krull-Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Green equivalence and Green correspondence known in…

We conjecture the existence of almost integer invariants governing the all-genus equivariant Gromov-Witten theory of Calabi-Yau fivefolds with a torus action. We prove the conjecture for skeletal, locally anti-diagonal torus actions by…

We consider equivariant versions of the motivic Chern and Hirzebruch characteristic classes of a quasi-projective toric variety, and extend many known results from non-equivariant to the equivariant setting. The corresponding generalized…

Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory quotient. This generalizes classical…

We define a certain class of simple varieties over a field $k$ by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if $k=\overline{k}$ and…

We consider the quotients $X = V/G$ of a symplectic complex vector space $V$ by a finite subgroup $G \subset Sp(V)$ which admit a smooth crepant resolution $Y \to X$. For such quotients, we prove the homological McKay correspondence…

Given a Hamiltonian torus action on a symplectic manifold, Teleman and Fukaya have proposed that the Fukaya category of each symplectic quotient should be equivalent to an equivariant Fukaya category of the original manifold. We lay out new…

Given an elliptic action of a compact Lie group $G$ on a co-oriented contact manifold $(M,E)$ one obtains two naturally associated objects: A $G$-transversally elliptic operator $\dirac$, and an equivariant differential form with…

In this paper, using the quantum McKay correspondence, we construct the "derived category" of G-equivariant sheaves on the quantum projective line at a root of unity. More precisely, we use the representation theory of U_{q}sl(2) at root of…

Wall-crossing formulas for various flavors of elliptic genus can be obtained using master spaces. We give a topological criterion which implies that such wall-crossing formulas are trivial. Applications are given for: GIT quotients,…

For a complex variety with a torus action we propose a new method of computing Chern-Schwartz-MacPherson classes. The method does not apply resolution of singularities. It is based on Localization Theorem in equivariant cohomology.

We explain the relationship between the sigma orientation and Witten genus on the one hand and the two-variable elliptic genus on the other. We show that if E is an elliptic spectrum, then the Theorem of the Cube implies the existence of…

This expository note surveys some results on equivariant K-theory of varieties with a torus action, focusing on recent work with Sam Payne and Richard Gonzales. It is based on my contribution to the Clifford Lectures at Tulane University in…

Let M be a quasiprojective algebraic manifold with K_M=0 and G a finite automorphism group of M acting trivially on the canonical class K_M; for example, a subgroup G of SL(n,C) acting on C^n in the obvious way. We aim to study the quotient…