Title: Scheme-theoretic Whitney conditions and applications to tangency of projective varieties,
Abstract: We investigate a scheme-theoretic variant of Whitney condition a. If X is a
projec-tive variety over the field of complex numbers and Y $\subset$ X a
subvariety, then X satisfies generically the scheme-theoretic Whitney condition
a along Y provided that the pro-jective dual of X is smooth. We give
applications to tangency of projective varieties over C and to convex real
algebraic geometry. In particular, we prove a Bertini-type theorem for
osculating plane of smooth complex space curves and a generalization of a
Theorem of Ranestad and Sturmfels describing the algebraic boundary of an
affine compact real variety.