Related papers: Cubic Extremal Transition and Gromov-Witten Theory

The abelian-nonabelian correspondence outlined by Bertram, Ciocan-Fontanine, and Kim gives a broad conjectural relationship between (twisted) Gromov-Witten invariants of related GIT quotients. This paper proves a case of the correspondence…

We define Gromov-Witten classes and invariants of smooth proper tame Deligne-Mumford stacks of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth proper…

This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.

For any finite abelian group G, the equivariant Gromov-Witten invariants of C^r/G can be viewed as a certain kind of abelian Hurwitz-Hodge integrals. In this note, we use Tseng's orbifold quantum Riemann-Roch theorem to express this kind of…

We prove a crepant transformation correspondence in genus zero Gromov-Witten theory for toric stack bundles related by crepant wall-crossings of the toric fibers. Specifically, we construct a symplectic transformation that identifies…

We prove the Abelian/non-Abelian Correspondence with bundles for target spaces that are partial flag bundles, combining and generalising results by Ciocan-Fontanine-Kim-Sabbah, Brown, and Oh. From this we deduce how genus-zero Gromov-Witten…

We construct and study the reduced, relative, genus one Gromov--Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov--Witten theory in genus one and are relative versions of…

In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form $Y_1\cup_D Y_2$ that arises from a degeneration $W/{\Bbb A}^1$ and a theory of relative…

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the…

This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.

We present a recursive algorithm computing all the genus-zero Gromov-Witten invariants from a finite number of initial ones, for Fano varieties with generically tame semi-simple quantum (and small quantum) (p, p)- type cohomology, whose…

An effective algorithm of determining Gromov--Witten invariants of smooth hypersurfaces in any genus (subject to a degree bound) from Gromov--Witten invariants of the ambient space is proposed. The Appendix is joint with E. Schulte-Geers.

In this paper, we study some vanishing identities for Gromov-Witten invariants conjectured by K. Liu and H. Xu. We will prove these conjectures in the case that the summation range is large compare to genus. In fact, in such cases, we can…

In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mumford stacks.

In this article we propose a definition of super Gromov-Witten invariants by postulating a torus localization property for the odd directions of the moduli spaces of super stable maps and super stable curves of genus zero. That is, we…

We give an explicit formula for (T-equivariant) 3-pointed genus zero Gromov-Witten invariants for G/B. We derive it by finding an explicit formula for the equivariant Pontryagin product on the homology of the based loop group \Omega K.

We introduce K-theoretic Gromov-Witten invariants of algebraic orbifold target spaces. Using the methods developed by Givental-Tonita we characterize Giventals Lagrangian cone of quantum K theory of orbifolds in terms of the cohomological…

We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these…

K-theoretic Gromov-Witten invariants of a compact Kahler manifold $X$ are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. With this article, we begin a series…

We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the…