Lycka Drakengren: Precise parameterization for the period map

Abstract: I will explain how we can find the Taylor expansion for the period map for curves under arbitrary local deformations. For a curve which is smooth, or more generally of compact type, these deformations can be obtained as combinations of Schiffer variations and shifts or smoothings of nodes. The method generalizes earlier work by Hu-Norton, Schiffer, Wolpert, Yamada and more, and the fundamental bidifferential plays an important role. I will also mention some applications, both affirmative and speculative.