Focal Loci of Algebraic Varieties I
نویسنده
چکیده
The focal locus X of an aane variety X is roughly speaking the (projective) closure of the set of points O for which there is a smooth point x 2 X and a circle with centre O passing through x which os-culates X in x. Algebraic geometry interprets the focal locus as the branching locus of the endpoint map between the Euclidean normal bundle N X and the projective ambient space (sends the normal vector O ?x to its endpoint O), and in this paper we address two general problems : 1) Characterize the "degenerate" case where the focal locus is not a hypersurface 2) Calculate, in the case where X is a hypersurface, its degree (with multiplicity)
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