The projective geometry of Freudenthal's magic square

J. M. Landsberg; L. Manivel

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arXiv · math/9908039

The projective geometry of Freudenthal's magic square

J. M. Landsberg·L. Manivel

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Abstract

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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BibTeX RIS

J. M. Landsberg, L. Manivel. 1999-08-10. The projective geometry of Freudenthal's magic square. https://arxiv.org/abs/math/9908039

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