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arXiv · 1308.0745

On the varieties of the second row of the split Freudenthal-Tits Magic Square

Jeroen Schillewaert·Hendrik Van Maldeghem
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Abstract

Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e.~the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in 8-di\-men\-sional projective spaces, the line Grassmannians in 14-dimensional projective spaces, and the exceptional varieties of type $\mathsf{E}_{6}$ in 26-dimensional projective space. Our theorem can be regarded as a far-reaching generalization of Mazzocca and Melone's approach to finite quadric Veronesean varieties. This approach takes projective properties of complex Severi varieties as smooth varieties as axioms.

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BibTeXRIS

Jeroen Schillewaert, Hendrik Van Maldeghem. 2016-12-20. On the varieties of the second row of the split Freudenthal-Tits Magic Square. https://arxiv.org/abs/1308.0745

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