Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points

Algebra Seminar
Monday, December 5, 2016 - 16:15
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality. We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus.