The projective geometry of Freudenthal's magic square

Details The projective geometry of Freudenthal's magic square The projective geometry of Freudenthal's magic square

1999-08-10

arxiv.org/abs/math/9908039v1

Mathematics

Algebraic Geometry

30 pages, LaTeX2e

Scientific paper

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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