Relative GromovWitten invariants and the mirror formula
Abstract
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that K_Y is nef. Using the technique of relative GromovWitten invariants, we give a new short and geometric proof of (a version of) the "mirror formula", i.e. we show that the generating function of the genus zero 1point GromovWitten invariants of Y can be obtained from that of X by a certain change of variables (the socalled "mirror transformation"). Moreover, we use the same techniques to give a similar expression for the (virtual) numbers of degreed plane rational curves meeting a smooth cubic at one point with multiplicity 3d, which play a role in local mirror symmetry.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2000
 arXiv:
 arXiv:math/0009190
 Bibcode:
 2000math......9190G
 Keywords:

 Algebraic Geometry
 EPrint:
 16 pages