English

Bad reduction of genus $3$ curves with complex multiplication

Number Theory 2014-12-11 v2 Algebraic Geometry

Abstract

Let CC be a smooth, absolutely irreducible genus-33 curve over a number field MM. Suppose that the Jacobian of CC has complex multiplication by a sextic CM-field KK. Suppose further that KK contains no imaginary quadratic subfield. We give a bound on the primes p\mathfrak{p} of MM such that the stable reduction of CC at p\mathfrak{p} contains three irreducible components of genus 11.

Keywords

Cite

@article{arxiv.1407.3589,
  title  = {Bad reduction of genus $3$ curves with complex multiplication},
  author = {Irene Bouw and Jenny Cooley and Kristin Lauter and Elisa Lorenzo Garcia and Michelle Manes and Rachel Newton and Ekin Ozman},
  journal= {arXiv preprint arXiv:1407.3589},
  year   = {2014}
}