Related papers: Elliptic Virtual Structure Constants and Gromov-Wi…
As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component $\ov\M_{1,k}^0(\P,d)$ of the moduli space of stable genus-one holomorphic maps into $\P$ have a well-defined euler…
In this paper, we propose a conjecture that clarifies the relationship between the number of degree d elliptic curves in complex four-dimensional projective Fano hypersurfaces and their degree d elliptic Gromov-Witten (GW) invariants. The…
In this paper, we propose a method for computing genus 1 Gromov-Witten invariants of Calabi-Yau and Fano projective hypersurfaces using the B-model. Our formalism is applicable to both Calabi-Yau and Fano cases. In the Calabi-Yau case,…
In this paper, we generalize Walcher's computation of the open Gromov-Witten invariants of the quintic hypersurface to Fano and Calabi-Yau projective hypersurfaces. Our main tool is the open virtual structure constants. We also propose the…
We recursively compute the Gromov-Witten invariants of the Hilbert scheme of two points in the plane. By studying the space of stable maps and computing virtual contributions, we use these invariants to enumerate hyperelliptic plane curves…
In this paper, we propose a geometrical approach to mirror computation of genus 0 Gromov-Witten invariants of CP^2. We use multi-point virtual structure constants, which are defined as intersection numbers of a compact moduli space of quasi…
We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums…
We extend B. Hassett's theory of weighted stable pointed curves ([Has03]) to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing phenomenon studied. This can be considered as a non-linear…
In this paper, we propose another characterization of the generalized mirror transformation on the quantum cohomology rings of general type projective hypersurfaces. This characterics is useful for explicit determination of the form of the…
We describe the structure of mirror formulas for genus 0 Gromov-Witten invariants of projective complete intersections with any number of marked points and provide an explicit algorithm for obtaining the relevant structure coefficients. The…
In this paper, we discuss some applications of Givental's differential equations to enumerative problems on rational curves in projective hypersurfaces. Using this method, we prove some of the conjectures on the structure constants of…
Let Y be a Calabi-Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the twisted I-function is one-dimensional, and spanned by the Gram matrix…
We define Gromov--Witten invariants of exploded manifolds. The technical heart of this paper is a construction of a virtual fundamental class $[\mathcal K]$ of any Kuranishi category $\mathcal K$ (which is a simplified, more general version…
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
We compute the integral torus-equivariant cohomology ring for weighted projective space for two different torus actions by embedding the cohomology in a sum of polynomial rings $\oplus_{i=0}^n \Z[t_1, t_2,..., t_n]$. One torus action gives…
We define a notion of a symplectic structure on stratified spaces, and demonstrate that given a symplectic structure on a stratified space $X$ with integral cohomology class, $X$ can be symplectically embedded in some complex projective…
The first part of this work constructs real positive-genus Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the second part studies the orientations on the moduli spaces of real maps used in…
We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every…
In our previous work, we provided an algebraic proof of the Zinger's comparison formula between genus one Gromov-Witten invariants and reduced invariants when the target space is a complete intersection of dimension two or three in a…
We show that moduli spaces of stable maps admits virtual orbifold structure. The symplectic version of virtual localization formula is obtained.