Bulletin of the Belgian Mathematical Society - Simon Stevin

Quadric Veronesean Caps

J. Schillewaert and H. Van Maldeghem

Full-text: Open access

Abstract

In 2008, Ferrara Dentice and Marino provided a characterization theorem for Veronesean caps in $\mathsf{PG}(N,\mathbb{K})$, with $\mathbb{K}$ a skewfield. This result extends the theorem for the finite case proved by J.A. Thas and Van Maldeghem in 2004. However, although the statement of this theorem is correct, the proof given by Ferrara Dentice and Marino is incomplete, as they borrow some lemmas from the paper of J.A. Thas and Van Maldeghem, which are proved using counting arguments and hence require a different approach in the infinite case. In this paper we use the Veblen-Young theorem to fill these gaps. Moreover, we then use this classification of Veronesean caps to provide a further general geometric characterization.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 1 (2013), 19-25.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1366306711

Digital Object Identifier
doi:10.36045/bbms/1366306711

Mathematical Reviews number (MathSciNet)
MR3082740

Zentralblatt MATH identifier
1271.51001

Subjects
Primary: 51A24

Keywords
Quadric Veronesean embedding

Citation

Schillewaert, J.; Van Maldeghem, H. Quadric Veronesean Caps. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 1, 19--25. doi:10.36045/bbms/1366306711. https://projecteuclid.org/euclid.bbms/1366306711


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