REDUCED GENUS-ONE GROMOV-WITTEN INVARIANTS

摘要

In a previous paper, we described a natural closed subset, (M) over bar (0)(1,k) (X, A; J), of the moduli space (M) over bar (1,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 and conclude that (M) over bar (0)(1,k) (X, A; J), just like (M) over bar (1,k) (X, A; J), carries a virtual fundamental class, which can be used to define symplectic invariants. These truly genus-one invariants constitute part of the standard genus-one Gromov-Witten invariants, which arise from the entire moduli space (M) over bar (1,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.