A geometrical theory of Jacobi forms of higher degree

초록

The purpose of this paper is to give a survey of a geometrical theory of Jacobi forms of higher degree. The author also gives some geometric problems which should be investigated in the future. The contents of this paper are as follows: 1. Introduction: 2. Jacobi forms: 3. Historical remarks: 4. Review on toroidal compactifications of the Siegel space and the universal abelian variety: 5. The automorphic vector bundle $E_{\rho ,WCalM}$: 6. Smooth compactification of Siegel moduli spaces and open problems: 7. The boundary of the Satake compactification: 8. Singular Jacobi forms: 9. The Siegel-Jacobi operator: 10. Final remarks: [Appendix A]. Subvarieties of the Siegel modular variety: [Appendix B]. Singular modular forms.