Related papers: Mirror theorems for root stacks and relative pairs

Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov--Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and…

By considering the partition function of the topological 2D gravity, a conformal field theory on the Airy curve emerges as the mirror theory of Gromov-Witten theory of a point. In particular, a formula for bosonic n-point functions in terms…

We study Givental's Lagrangian cone for the quantum orbifold cohomology of toric stack bundles and prove that the I-function gives points in the Lagrangian cone, namely we construct an explicit slice of the Lagrangian cone defined by the…

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open…

Given a smooth log Calabi--Yau pair $(X,D)$, we use the intrinsic mirror symmetry construction to define the mirror proper Landau--Ginzburg potential and show that it is a generating function of two-point relative Gromov--Witten invariants…

Mirror symmetry gives predictions for the genus zero Gromov-Witten invariants of a closed Calabi--Yau variety in terms of period integrals on a mirror family of Calabi-Yau varieties. We deduce an analogous mirror theorem for the open…

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 introduce marked relative Pandharipande-Thomas (PT) invariants for a pair $(X,D)$ of a smooth projective threefold and a smooth divisor. These invariants are defined by integration over the moduli space of $r$-marked stable pairs on…

This expository article is an introduction to logarithmic Gromov--Witten (GW) theory. We discuss how to study the GW theory of a smooth projective variety via simple normal crossings degenerations. We survey several approaches to…

This is the second part of the paper "A degeneration of stable morphisms and relative stable morphisms", (math.AG/0009097). In this paper, we constructed the relative Gromov-Witten invariants of a pair of a smooth variety and a smooth…

We represent stationary descendant Gromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of large degree behaviour of stationary descendant…

A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space X = G/P. When X is cominuscule we prove that the map from a related Gromov-Witten variety…

Let $X$ be a smooth complex projective algebraic variety. Let $\mathcal{G}$ be a $G$-banded gerbe with $G$ a finite abelian group. We prove an exact formula expressing genus $g$ orbifold Gromov-Witten invariants of $\mathcal{G}$ in terms of…

The introduction is modified in the revised version. Also, many typos and errors were corrected. Let $W\to C$ be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed…

The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs $(X,D)$ of a variety $X$ and a divisor $D$. We develop a generalization of this theory…

We give two proofs of a conjecture of Hori and Vafa which expresses the J-function (i.e, the generating function for 1-point descendant Gromov-Witten invariants) of a Grassmannian in terms of the J-function of a product of projective…

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

In this paper, we proved generating functions of Gromov-Witten cycles of the elliptic orbifold lines with weights (3,3,3), (4,4,2), and (6,3,2) are cycle-valued quasi-modular forms. This is a generalization of Milanov and Ruan's work on…

Given $\mathfrak{F}$ a coherent sheaf on a Noetherian integral algebraic stack $\mathfrak{P}$, we give two constructions of stacks $\widetilde{\mathfrak{P}}$, equipped with birational morphisms $p:\widetilde{\mathfrak{P}}\to \mathfrak{P}$…

We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…