Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

José Ignacio Burgos Gil

The arithmetic degree of the line bundle of Siegel-Jacobi modular forms

Abstract: The singularities of the line bundle of Siegel-Jacobi modular forms are not logarithmic and the usual techniques to deal with automorphic vector bundles on pure Shimura varieties do not apply. Yuan and Zhang have proved that this singular line bundle is an example of adelic line bundle on a quasi-projective variety.
Nevertheless it is not clear whether this line bundle is integrable, so the techniques of Yuan and Zhang also do not apply. We will show how to use the recent development on relative finite energy singularities by Darvas, Di Nezza and Lu to extend Yuan and Zhang intersection product to cover the line bundle of Siegel-Jacobi modular forms and using its functorial properties we will compute its arithmetic degree. This is joint work with J. Kramer.