Veronese and Segre varieties

  • J. W. P. Hirschfeld
  • J. A. Thas
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The Veronese variety of all quadrics of \(PG(n, K), n \geq 1\), is the variety
$$\mathcal{V} = \left\{{\bf P}(x_0^2,x_1^2,\ldots,x_n^2,x_0x_1,\ldots,x_0x_n,x_1x_2,\ldots,x_1x_n,\ldots,x_{n-1}x_n)| {\bf P}(X) \mathrm{is\; a\; point\; of\; PG(\it n,K)}\right\}$$
of \(PG( N, K)\) with \(N \;=\;n(n+3)/2\), where \(X\;=\;(x_0,x_1,\ldots,x_n)\); then V is a variety of dimension n.

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Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • J. W. P. Hirschfeld
    • 1
  • J. A. Thas
    • 2
  1. 1.Department of MathematicsUniversity of SussexBrightonUK
  2. 2.Department of MathematicsGhent UniversityGentBelgium

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