On the dimensions of secant varieties of Segre-Veronese varieties

By Hirotachi Abo, Maria Chiara Brambilla. 2009

58 citations recorded by the source corpus.

This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high-dimensional case to the computation of the dimensions of secant varieties in low-dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective sth Segre–Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre–Veronese varieties.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/43333605cd481e21d1d9403dcb0746a8ec75c6d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Alessandra Bernardi
2. A. Oneto
3. Alessandro Gimigliano
4. Enrico Carlini
5. M. Catalisano

In Computational Mechanics

1. Alessandra Bernardi

In Computational Theory and Mathematics

1. Alessandra Bernardi
2. M. Catalisano
3. A. Oneto
4. Alessandro Gimigliano
5. Enrico Carlini

Citations in the corpus

• The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “When it comes to Segre–Veronese varieties with only two factors, there are many results by many authors, which allow us to get a quite complete picture, described by the following conjectures, as stated in [121].”