Related papers: Structures in genus-zero relative Gromov--Witten t…
We define Gromov-Witten classes and invariants of smooth projective schemes of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth projective scheme over…
We state and prove a topological recursion relation that expresses any genus-g Gromov-Witten invariant of a projective manifold with at least a (3g-1)-st power of a cotangent line class in terms of invariants with fewer cotangent line…
We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…
We develop a formalism for relative Gromov-Witten invariants of Li that is analogous to the Symplectic Field Theory of Eliashberg, Givental, and Hofer. This formalism allows us to express natural degeneration formulae in terms of generating…
We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete…
A Kuranishi atlas is a structure used to build a virtual fundamental class on moduli spaces of $J$-holomorphic curves. They were introduced by McDuff and Wehrheim to resolve some of the challenges in this field. This paper completes the…
For smooth projective G-varieties, we equate the gauged Gromov-Witten invariants for sufficiently small area and genus zero with the invariant part of equivariant Gromov-Witten invariants. As an application we deduce a gauged version of…
In this article, we study the change of genus zero Gromov-Witten invariants under Type II extremal transitions in degree 4.
We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these two approaches yields nontrivial…
We introduce Gromov-Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov-Witten invariants with naive tangency conditions in terms of…
Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible multiplicative characteristic class. Special cases…
We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated open Gromov-Witten invariants of a Lagrangian submanifold $L \subset X$ with a bounding chain. Simultaneously, we define the…
This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology of a smooth polarized complex projective variety with the action of a connected complex reductive…
We give a proof of a result of D. Peterson's identifying the quantum cohomology ring of a Grassmannian with the reduced coordinate ring of a certain subvariety of $GL_n$. The totally positive part of this subvariety is then constructed and…
We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for…
We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about Gromov-Witten invariants of compact…
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 characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, anti-holomorphic involution, then the…
Given a closed symplectic manifold $X$, we construct Gromov-Witten-type invariants valued both in (complex) $K$-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is $K_p(n)$-local for some Morava $K$-theory $K_p(n)$.…