Severi's theorem for d-uple Veronese varieties

2014/06/12 by Jeroen Schillewaert, Schillewaert, Jeroen, Koen Struyve +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #Tensor decomposition and applications #math.AG

paper · pdf · doi:10.48550/arxiv.1406.3256

arxiv created 2014/06/12 · openalex publication_date 2014/06/12 · arxiv updated 2014/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize d-uple Veronese embeddings of finite-dimensional projective spaces. The easiest non-trivial instance of our theorem is the embedding of the projective plane in 5-dimensional projective space, a result obtained in 1901 by Severi when the underlying field is complex.

Related

• On the varieties of the second row of the split Freudenthal-Tits Magic Square
• Osculating Varieties of Veronesean and their higher secant varieties
• Secant varieties of Segre-Veronese embeddings of (P¹)^r
• Osculating spaces to secant varieties
• Conjectures and computations about Veronese syzygies