New examples of defective secant varieties of Segre-Veronese varieties

TL;DR

This paper establishes the existence of previously unknown defective secant varieties in certain multi-degree Segre-Veronese varieties, advancing the classification of these geometric objects.

Contribution

It introduces new examples of defective secant varieties for three-factor and four-factor Segre-Veronese varieties, expanding the understanding of their geometric properties.

Findings

Existence of new defective secant varieties proven

Identification of defective varieties in specific multi-degree embeddings

Contribution to classification of secant varieties with multiple factors

Abstract

We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the classification of defective secant varieties of Segre-Veronese varieties with three or more factors.