International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 3, Pages 159-197

Mirror symmetry for concavex vector bundles on projective spaces

Artur Elezi

Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, Washington DC 20016, USA

Received 20 December 2001

Copyright © 2003 Artur Elezi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let XY be smooth, projective manifolds. Assume that ι:Xs is the zero locus of a generic section of V+=iI𝒪(ki), where all the ki's are positive. Assume furthermore that 𝒩X/Y=ι(V), where V=jJ𝒪(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 s. This leads to local mirror symmetry on the A-side.