Related papers: Equivariant holomorphic anomaly equation
We study the fundamental relationship between stable quotient invariants and the B-model for local CP2 in all genera. Our main result is a direct geometric proof of the holomorphic anomaly equation in the precise form predicted by B-model…
We define a formal Gromov-Witten theory of the quintic 3-fold via localization on CP4. Our main result is a direct geometric proof of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model…
We study the orbifold Gromov-Witten theory of the quotient C^3/Z_3 in all genera. Our first result is a proof of the holomorphic anomaly equations in the precise form predicted by B-model physics. Our second result is an exact crepant…
We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These…
In this paper, we prove finite generation property and holomorphic anomaly equation for the equivariant Gromov-Witten theory of $K_{\mathbb{P}^1\times\mathbb{P}^1}$.
We study the structure of higher genus Gromov-Witten theory of the quotient stack $[\mathbb{C}^n/\mathbb{Z}_n]$. We prove holomorphic anomaly equations for $[\mathbb{C}^n/\mathbb{Z}_n]$, generalizing previous results of Lho-Pandharipande…
Several properties of a hyepergeometric series related to Gromov-Witten theory of some Calabi-Yau geometries was studied in [8]. These properties play basic role in the study of higher genus Gromov-Witten theories. We extend the results of…
We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,\beta)$ to the locus where $\theta$ degenerates; it then enables us to define the…
In this paper, we prove quasi-modularity property for the twisted Gromov-Witten theory of $\mathcal{O}(3)$ over $\mathbb{P}^2$. Meanwhile, we derive its holomorphic anomaly equation.
We study the Gromov-Witten theory of $K_{\mathsf{P}^1\times\mathsf{P}^1}$ and some Calabi-Yau hypersurface in toric variety. We give a direct geometric proof of the holomorphic anomaly euqation for $K_{\mathsf{P}^1\times\mathsf{P}^1}$ in…
The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…
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…
We give a complete solution for the reduced Gromov-Witten theory of resolved surface singularities of type A_n, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the T-equivariant relative…
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…
For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow…
We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is governed by the 2-Toda hierarchy of Ueno and…
We use a topological framework to study descendent Gromov-Witten theory in higher genus, non-toric settings. Two geometries are considered: surfaces of general type and the Enriques Calabi-Yau threefold. We conjecture closed formulas for…
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…
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 the most general to date version of the permutation-equivariant quantum K-theory, and express its total descendant potential in terms of cohomological Gromov-Witten invariants. This is the higher-genus analogue of adelic…