Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras

초록

Given a mirror pair of a symplectic manifold X and a Landau-Ginzburg potential W, we are interested in whether the quantum cohomology of X and the Jacobian algebra of W are isomorphic. Since those can be equipped with Frobenius algebra structures, we might ask whether they are isomorphic as Frobenius algebras. We show that the Kodaira-Spencer map gives a Frobenius algebra isomorphism for elliptic orbispheres, under the Floer theoretic modification of the residue pairing.

키워드