Secant Varieties and Successive Minima. Appendix: On Linear Subspaces Contained in the Secant Varieties of a Projective Curve.

摘要

The paper is organized as follows. In Section 1 the authors compute the degree of the secant varieties and they give Voisin's result on secant varieties of curves (Th. 1). The authors deduce from it a geometric result on extension classes in Theorem 2. In Section 2 the authors propose another approach to linear subspaces in secant varieties of curves. Though weaker than Theorem 1, it might be of independent interest, especially because of Theorem 3, due to A. Granville. Granville's result computes the maximal length of a sequence of binominal coefficients, in a given line of Pascal's triangle, which have a common divisor. The answer turns out to be related to the distribution of primes among positive integers.