On the genus-one Gromov-Witten invariants of complete intersections
68 citations recorded by the source corpus.
We state and prove a long-elusive relation between genus-one Gromov-Witten of a complete intersection and twisted Gromov-Witten invariants of the ambient projective space. As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component M 0 1,k(P , d) of the moduli space of stable genus-one holomorphic maps into P have a well-defined euler class. In this paper, we extend this result to moduli spaces of perturbed, in a restricted way, J-holomorphic maps. This extension is used to show that these cones are the correct genus-one analogues of the vector bundles relating genus-zero Gromov-Witten invariants of a complete intersection to those of the ambient projective space. A relationship for highergenus invariants is conjectured as well.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/39fe9f06c82d40934386ec0026d94b8549005a6b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
Citations in the corpus
- Standard versus reduced genus-one Gromov–Witten invariants (2007, background): “In contrast, the failure of the expected hyperplane relation for genus-one invariants is addressed in [Z3] and [ LZ ] by dening reduced genus-one GW-invariants and showing that these invariants do satisfy the hyperplane relation, respectively.”
- Reduced genus-one Gromov-Witten invariants (2005, methodology): “In particular, Li and the author show in [ LZ ] that there is a simple relation between reduced genus-one GW-invariants of a projective complete intersection and twisted reduced genus-one GW-invariants of the ambient space.”