Keno Eilers (Oldenburg)

19/06/2014 - W01 0-006 (Wechloy), 4 pm c.t.

Calculating $\kappa$: Periods of second kind differentials of (n, s)-curves

For elliptic curves expressions for the periods of elliptic integrals of the second kind in terms of theta constants have been known since the middle of the 19th century. In this talk I consider the problem of generalising these results to curves of higher genera, in particular to a special class of algebraic curves, the so-called (n, s)-curves. It is shown that the representations required can be obtained in two ways: The first uses the comparison of two equivalent expressions for the projective connection and the second involves the general solution of the Jacobi inversion problem. By that we obtain not only the desired generalisation, but also a couple of relations of derivatives of theta constants.