Abstract
The focal locus is traditionally defined for a differentiable submanifold of Rn. However, since it depends essentially only on the notion of orthogonality, a focal locus can be also associated to an algebraic subvariety of the space \(P_C^n \), once we have chosen an orthogonal structure on this space. In this paper, we establish somebasic results in the theory of focal loci of algebraichypersurfaces in \(P_C^n \). Our main results concern the irreducibility of the ramification divisor of the end-point map and the dimension of the singular locus of this divisor, the birationality of the focal map and the degree of the focal locus of an algebraic hypersurface.
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