On the Singular Loci of Higher Secant Varieties of Veronese Embeddings
Year: 2025
Type: book-chapter
Abstract: The π-th secant variety of a projective variety X β P N X\subset\mathbb{P}^{N} , denoted by Ο k β’ ( X ) \sigma_{k}(X) , is defined to be the closure of the union of ( k β 1 ) (k-1) -planes spanned by π points on π. In this paper, we examine the π-th secant variety Ο k β’ ( v d β’ ( P n ) ) β P N \sigma_{k}(v_{d}(\mathbb{P}^{n}))\subset\mathbb{P}^{N} of the image of the π-uple Veronese embedding v d v_{d} of P n \mathbb{P}^{n} to P N \mathbb{P}^{N} with N = ( n + d d ) β 1 N=\binom{n+d}{d}-1 , and focus on the singular locus of Ο k β’ ( v d β’ ( P n )
Source: Chapman & Hall/CRC eBooks
Authors: Katsuhisa Furukawa, Kangjin Han
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4225827744