Mirror symmetry for concavex vector bundles on projective spaces

Abstract

LetX⊂Ybe smooth, projective manifolds. Assume thatι:X→ℙsis the zero locus of a generic section ofV+=⊕i∈I𝒪(ki), where all theki's are positive. Assume furthermore that𝒩X/Y=ι∗(V−), whereV−=⊕j∈J𝒪(−lj)and all thelj's are negative. We show that under appropriate restrictions, the generalized Gromov-Witten invariants ofXinherited fromYcan be calculated via a modified Gromov-Witten theory onℙs. This leads to local mirror symmetry on theA-side.