Veronese and Segre varieties View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2016-02-04

AUTHORS

J. W. P. Hirschfeld , J. A. Thas

ABSTRACT

The Veronese variety of all quadrics of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$PG(n, K), n \geq 1$$ \end{document}, is the variety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{V} = \left\{{\bf P}(x_0^2,x_1^2,\ldots,x_n^2,x_0x_1,\ldots,x_0x_n,x_1x_2,\ldots,x_1x_n,\ldots,x_{n-1}x_n)| {\bf P}(X) \mathrm{is\; a\; point\; of\; PG(\it n,K)}\right\}$$ \end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$PG( N, K)$$ \end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$N \;=\;n(n+3)/2$$ \end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$X\;=\;(x_0,x_1,\ldots,x_n)$$ \end{document}; then V is a variety of dimension n. More... »

PAGES

143-221

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4471-6790-7_4

DOI

http://dx.doi.org/10.1007/978-1-4471-6790-7_4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1026604729


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