摘要
In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers coordinates.This generalizes fully the famous Rauch's variational formula.As applications,we compute the curvature of Siegel metric at point [X] with Π([X]) =√ -1 Ig and the Christoffel symbols of L2-induced Bergman metric on Mg.
In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers coordinates.This generalizes fully the famous Rauch’s variational formula.As applications,we compute the curvature of Siegel metric at point [X] with Π([X]) =√ -1 Ig and the Christoffel symbols of L2-induced Bergman metric on Mg.
