Numerical Analysis/Differential Geometry General formulas for the smoothed analysis of condition numbers

We provide estimates on the volume of tubular neighborhoods around a subvariety Σ of real projective space, intersected with a disk of radius σ . The bounds are in terms of σ , the dimension of the ambient space, and the degree of equations defining Σ .W e use these bounds to obtain smoothed analysis estimates for some conic condition numbers. To cite this article: P. Bürgisser et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).