The Brill-Segre formula and the abc conjecture
The Brill-Segre formula counts the number of osculation points for a
morphism of a curve to n-dimensional space and generalizes the Hurwitz
formula (n=1) and the Plucker formula (n=2). The Brill-Segre 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
Brill-Segre formula. The talks will discuss these topics.
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