1998/03/12 by Alexander Givental, Givental, Alexander B. · 15 citations
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/9803053
A conjecture expressing genus 1 Gromov-Witten invariants in mirror-theoretic\nterms of semi-simple Frobenius structures and complex oscillating integrals is\nformulated. The proof of the conjecture is given for torus-equivariant Gromov -\nWitten invariants of compact K "ahler manifolds with isolated fixed points and\nfor concave bundle spaces over such manifolds. Several results on genus 0\nGromov - Witten theory include: a non-linear Serre duality theorem, its\napplication to the genus 0 mirror conjecture, a mirror theorem for concave\nbundle spaces over toric manifolds generalizing a recent result of B. Lian, K.\nLiu and S.-T. Yau. We also establish a correspondence (see the extensive\nfootnote in section 4) between their new proof of the genus 0 mirror conjecture\nfor quintic 3-folds and our proof of the same conjecture given two years ago.\n