Mirror symmetry for concavex vector bundles on projective spaces

Let X⊂Y be smooth, projective manifolds. Assume that ι:X→ℙs is the zero locus of a generic section of V+=⊕i∈IðÂ’ª(ki), where all the ki's are positive. Assume furthermore that ðÂ’©X/Y=ι∗(V−), where V−=⊕j∈JðÂ’ª(−lj) and all the lj's are negative. We show that under appropriate restrictions, the generalized Gromov-Witten invariants of X inherited from Y can be calculated via a modified Gromov-Witten theory on ℙs. This leads to local mirror symmetry on the A-side