In our previous work, we provided an algebraic proof of the Zingers 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 projective space. In this paper, we extend the result in any dimensions and for descendant invariants.
We show that it is possible to define the contribution of degree one covers of a disk to open Gromov-Witten invariants. We build explicit sections of obstruction bundles in order to extend the algebro-geometric techniques of Pandharipande to the case of domains with boundary.
We give a formula computing the number of one-nodal rational curves that pass through an appropriate collection of constraints in a complex projective space. We combine the methods and results from three different papers.
We construct a sheaf of Fock spaces over the moduli space of elliptic curves E_y with Gamma_1(3)-level structure, arising from geometric quantization of H^1(E_y), and a global section of this Fock sheaf. The global section coincides, near appropriate limit points, with the Gromov-Witten potentials of local P^2 and of the orbifold C^3/mu_3. This proves that the Gromov-Witten potentials of local P^2 are quasi-modular functions for the group Gamma_1(3), as predicted by Aganagic-Bouchard-Klemm, and proves the Crepant Resolution Conjecture for [C^3/mu_3] in all genera.
We use the hyperKaler geometry define an disc-counting invariants with deformable boundary condition on hyperKahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon and are expected to be the generalized Donaldson-Thomas invariants in the construction of hyperKahler metric proposed by Gaiotto-Moore-Neitzke.
We propose a conjectural explicit formula of generating series of a new type for Gromov--Witten invariants of $mathbb{P}^1$ of all degrees in full genera.
Sanghyeon Lee
,Jeongseok Oh
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(2020)
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"Algebraic reduced genus one Gromov-Witten invariants for complete intersections in projective spaces, Part 2"
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Sanghyeon Lee
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