Terracini Loci, Linear Projections, and the Maximal Defect

Abstract

We continue the study of Terracini loci formed by x points of a variety embedded in a projective space. Our main results are a refined study of Terracini loci arising from linear projections, the description of the maximal x with a non-empty Terracini locus for Hirzebruch surfaces, and the maximal “weight”, “corank”, or “defect” in several cases. For low x, we even show which defects can occur.

Keywords

• Veronese variety
• Terracini set
• Hilbert function
• zero-dimensional scheme
• Hirzebruch surface