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The Projective Geometry of Freudenthal's Magic Square

✍ Scribed by J.M Landsberg; L Manivel

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 248 KB
Volume: 239
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8697

No coin nor oath required. For personal study only.

✦ Synopsis

We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations, and interpreting them in terms of composition algebras. In particular, we show how a class of invariant quartic polynomials can be viewed as generalizations of the classical discriminant of a cubic polynomial.

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