Focal loci of algebraic hypersurfaces: A general theory

Journal article

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 PnC, once we have chosen an orthogonal structure on this space. In this paper, we establish some basic results in the theory of focal loci of algebraic hypersurfaces in PnC. 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.

Authors: Trifogli, C

• Publication status: Published
• Journal: GEOMETRIAE DEDICATA
• Volume: 70
• Issue: 1
• Pages: 1-26
• Publication date: 1998-03-01
• DOI: 10.1023/A:1005059516044
• ISSN: 0046-5755
• Language: English
• Keywords: algebraic hypersurfaces; orthogonality; end-point map; focal loci