Let Hg and Dg be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let C be the Euclidean space of all h× g complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk Dg × C (h,g) onto the Siegel-Jacobi space Hg × C (h,g) which gives a partial bounded realization of Hg × C (h,g) by Dg ×C . We prove that the natural actions of the Jacobi g...

The goal of these lectures is twofold: first I would like to introduce the basic concepts of the theory, like the Siegel modular group and its action on the Siegel upper half-space, reduction theory, examples of Siegel modular forms, Hecke operators and L-functions. Secondly, following up, I would like to discuss two rather recent research topics, namely the ”Ikeda lifting” and sign changes of ...

X iv :m at h/ 00 12 20 2v 1 [ m at h. A G ] 2 0 D ec 2 00 0 The Moduli Space of Bilevel-6 Abelian Surfaces G.K. Sankaran & J. Spandaw The moduli space Abil t of (1, t)-polarised abelian surfaces with a weak bilevel structure was introduced by S. Mukai in [11]. Mukai showed that Abil t is rational for t = 2, 3, 4, 5. More generally, we may ask for birational invariants, such as Kodaira dimension...