Arithmetic of superelliptic curves

• Applicant: Professor Dr. Ulf Kühn
• Subject Area: Mathematics
• Term: from 2011 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 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 Programme: Research Grants