Discriminants and Artin conductors

Journal article, 2016

We study questions of multiplicities of discriminants for degenerations coming from projective duality over discrete valuation rings. The main observation is a type of discriminant-different formula in the sense of classical algebraic number theory, and we relate it to Artin conductors via Bloch's conjecture. In the case of discriminants of planar curves we can calculate the different precisely. In general these multiplicities encode topological invariants of the singular fibers and in the case of characteristic p, also wild ramification data in the form of Swan conductors. This builds upon results of T. Saito.