On secant defective varieties, in particular of dimension 4

TL;DR

This paper investigates secant defective varieties, especially in four dimensions, providing new classification results and extending classical work to better understand their geometric properties.

Contribution

It offers a complete classification of secant defective 4-folds, advancing the understanding of secant defectiveness in algebraic geometry.

Findings

Full classification of secant defective 4-folds

General results on secant defective varieties

Extension of classical results by G. Scorza

Abstract

In this paper we prove some general results on secant defective varieties. Then we focus on the 4--dimensional case and we give the full classification of secant defective 4--folds. This paper has been inspired by classical work by G. Scorza,