Arithmetic of superelliptic curves

• Antragsteller: Professor Dr. Ulf Kühn
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2011 bis 2016
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 203526262

In this project we want to estimate the arithmetic self intersection number ω-2 Ar of the relative dualizing sheaf varying in discrete families of arithmetic surfaces associated to superelliptic curves defined over number fields with fixed ramification. In general such estimates are of great interest in arithmetic intersection theory, since these invariants are intimately related to other major problems in arithmetic geometry, such as the effective Mordell conjecture or special values of L-series, but there are very few classes of curves for which estimates, or even bounds, on ω-2Ar are known. In order to obtain such estimates, we plan to compute upper bounds using a theorem of the applicant and lower bounds using techniques due to Zhang.

• DFG-Verfahren: Sachbeihilfen