Non-defectivity of Segre-Veronese varieties

TL;DR

This paper proves that Segre-Veronese varieties are not secant defective when each degree is at least three, using induction, and extends the result to certain cases with mixed degrees.

Contribution

It establishes a new non-defectivity result for Segre-Veronese varieties with degrees at least three, improving understanding of their secant properties.

Findings

Segre-Veronese varieties are never secant defective if all degrees ≥ 3

Inductive proof based on number of factors, degree, and dimension

Almost optimal non-defectivity result for mixed degree cases

Abstract

We prove that Segre-Veronese varieties are never secant defective if each degree is at least three. The proof is by induction on the number of factors, degree and dimension. As a corollary, we give an almost optimal non-defectivity result for Segre-Veronese varieties with one degree equal to one and all the others at least three.