Калмыков Артём Олегович
Mirror Symmetry for Jacobians of Hyperelliptic Curves
In this work, we construct a mirror family for the Jacobian of a hyperelliptic curve, examining in details the genus two case. More definitely, we propose a notion of a mirror family as the complex moduli space of a homological mirror together with an additional information, and compute its Picard-Fuchs equation and monodromy representation. Then we compute the (twisted) Givental J-function of the Jacobian by means of the abelian/nonabelian correspondence, and show that in some sense its coefficients are indeed the solutions to the Picard-Fuchs equation.