Ulf Kühn (Hamburg)

22 May 2014 - W01 0-006 (Wechloy), 4 pm c.t.

Analytic and algebraic geometric aspects of Jacobian forms

Analytic and algebraic geometric aspects of Jacobi forms Abstract: The Chern-Weil theory states that the algebraic intersection numbers of line bundles on varieties can be determined both algebraically geometrically and by calculating integrals, namely by means of the Chern form of a smooth metric. Mumford showed that the canonical metrics on Shimura varieties, although logarithmically singular, also have this important property. We will show this for the bundle of modular forms over the elliptic modular curve and explain why this property is not so easy to obtain for the straight line bundle of Jacobi forms on the universal elliptic curve. The paper is based on a joint work with J. Kramer and J.I. Burgos-Gil: arxiv.org/abs/1405.3075.