GENERIC INNER PROJECTIONS OF PROJECTIVE VARIETIES AND AN APPLICATION TO THE POSITIVITY OF DOUBLE POINT DIVISORS

摘要

Let X ? P~N be a smooth nondegenerate projective variety of dimension n ≥ 2, codimension e and degree d with the canonical line bundle ω_x defined over an algebraically closed field of characteristic zero. The purpose here is to prove that the base locus of O_x(d - n - e - 1) ? ω_x~v is at most a finite set, except in a few cases. To describe the exceptional cases, we classify (not necessarily smooth) projective varieties whose generic inner projections have exceptional divisors. As applications, we prove the (d - e)-regularity of Ox, Property (N_(k-d+e)) for O_x(k), and inequalities for the delta and sectional genera.