Reduced genus-one Gromov-Witten invariants

By A. Zinger. 2005

65 citations recorded by the source corpus.

In a previous paper we described a natural closed subset M 0 1,k(X,A; J) of the moduli space M1,k(X,A; J) of stable genus-one J-holomorphic maps into a symplectic manifold X. In this paper we generalize the definition of the main component to moduli spaces of perturbed, in a restricted way, J-holomorphic maps. This generalization implies that M 0 1,k(X,A; J), just like M1,k(X,A; J), carries a virtual fundamental class and can be used to define symplectic invariants. These truly genus-one invariants constitute part of the standard genus-one GromovWitten invariants, which arise from the entire moduli space M1,k(X,A; J). The new invariants are more geometric and can be used to compute the genus-one GW-invariants of complete intersections, as shown in a separate paper.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/375e5103e33702136379ee32c99c84198214e0fa

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In Geometry and Topology

1. A. Zinger
2. Bumsig Kim
3. Y. Ruan
4. A. Chiodo
5. P. Seidel

Citations in the corpus

• Standard versus reduced genus-one Gromov–Witten invariants (2007, methodology): “However, this is not part of the denition of reduced genus-one invariants and the relation described by Proposition 3.1 in [ Z3 ] is not convenient for immediate applications; see Proposition 3.2 below.”