On High G_k−1,k-Defective Varieties

Abstract

We give a rough characterization for n-dimensional varieties with G_k−1,k-defect equal to a > 0 if k ≥ n. Then we apply this in the case that a ≥ n − 2 to become a fine classification.

Key Words:

• Grassman-defectivity
• Secant variables

MSC:

• 14N15
• 14J40
• 14M15

ACKNOWLEDGMENTS

The author wishes to thank Marc Coppens for suggesting the subject of the article and some interesting ideas. His research was partially supported by the Fund of Scientific Research—Flanders (G.0318.06).

Notes

Communicated by L. Ein.