Representations of Kronecker forms at higher genus

by Artyom Lisitsyn (ETH Zurich)

Wednesday 3 Apr 2024, 13:00 → 14:00 Europe/Berlin

Wegelerstraße 10/2.019 (PI) - Seminar Room BCTP I (PI)

Polylogarithms can be represented as iterated integrals over differential forms generated by a Kronecker function, corresponding to a representation independent, quasiperiodic one-form with a simple pole. We study the space of such forms at higher genera, proving that the dimension of the space of such quasiperiodic forms does not exceed the genus, as well as giving constructive examples of higher genus Kronecker forms. Using a ratio of theta functions, we identify Kronecker forms satisfying a Fay identity. Using the uniformization provided by Schottky covers, we identify Kronecker forms that correspond to Enriquez' connection, with an implied degeneration procedure.