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**public sources and our publisher partners.**We show that certain hypergeometric series used to formulate mirror symmetry for Calabi-Yau hypersurfaces, in string theory and algebraic geometry, satisfy a number of interesting properties. Many of… Expand

0. Introduction 691 0.1. Mirror symmetry predictions for a quintic threefold 691 0.2. Computing GW-invariants of hypersurfaces 693 0.3. Mirror symmetry formulas for projective CY-hypersurfaces 695 1.… Expand

We construct a natural smooth compactification of the space of smooth genus-one curves with k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth… Expand

The moduli space of stable quotients introduced by Marian-Oprea-Pandharipande provides a natural compactification of the space of morphisms from nonsingular curves to a nonsingular projective variety… Expand

In this paper we exploit the geometric approach to the virtual fundamental class, due to Fukaya-Ono and Li-Tian, to compare the virtual fundamental classes of stable maps to a symplectic manifold and… Expand

We describe a natural isomorphism between the set of equivalence classes or pseudocycles and the integral homology groups of a smooth manifold. Our arguments generalize to settings well-suited for… Expand

We give an explicit formula for the difference between the standard and reduced genus-one Gromov‐Witten invariants. Combined with previous work on geometric properties of the latter, this paper makes… Expand

We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and… Expand

The main concrete result of this paper is enumeration of genus-two curves with complex structure fixed in P and P. Along the way, rational curves with certain simple singularities are counted as… Expand