The BrillSegre formula and the abc conjecture
The BrillSegre formula counts the number of osculation points for a
morphism of a curve to ndimensional space and generalizes the Hurwitz
formula (n=1) and the Plucker formula (n=2). The BrillSegre formula
implies the generalization of the abc theorem for function fields (due
to Mason) to arbitrarily many summands (proved by Brownawell, Masser
and Voloch). Smirnov has suggested a conjectural analogue of Hurwitz
formula for number fields which implies the abc conjecture. We hope to
be able to formulate a corresponding number field analogue of the
BrillSegre formula. The talks will discuss these topics.
