Objetivo In my thesis, I worked on compact quaternionic Shimura surfaces. Ideveloped techniques which made it possible to study particular casesof these surfaces and place them into the Kodaira classification of algebraic surfaces. In this proposal, I describe how these investigations can be extended in several directions and broadened toinvolve other research areas, in particular modular forms. With the techniques which are now available, it should be possible tosolve some types of problems which have previously been considered forHubert modular surfaces. For example, to classify all cases when the surface is rational, and to, in some particular cases, describe the surface up to isomorphism The connections with modular forms goes in several directions. One is to explore how the intersection numbers of cycles on the surfaces are related to coefficients of modular forms. Another direction is to study modular forms on compact Shimura varieties themselves. Progressing this area will lead to new results about the arithmetic of abeliansurfaces. Working at the Max Plank institute, with Prof. Harder and the other experts, will be a favourable environment to attain the new skills needed to fulfil these goals. Ámbito científico natural sciencesmathematicspure mathematicsarithmetics Palabras clave Kodaira classification Shimura surface modular form Programa(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Tema(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Convocatoria de propuestas FP6-2002-MOBILITY-5 Consulte otros proyectos de esta convocatoria Régimen de financiación EIF - Marie Curie actions-Intra-European Fellowships Coordinador MAX PLANCK GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V. Aportación de la UE Sin datos Dirección Hofgartenstrasse 8 101062 MUENCHEN Alemania Ver en el mapa Coste total Sin datos
