The geometries of the Freudenthal-Tits magic square
If you have a question about this talk, please contact David Craven.
I will discuss an ongoing project (joint with H. Van Maldeghem) to give a uniform axiomatic description of the embeddings in projective space of the varieties corresponding with the geometries of exceptional Lie type over arbitrary fields.
In particular, I will focus on the second row of the Freudenthal-Tits Magic Square.
I will mainly focus on the split case, and provide a uniform (incidence) geometric characterization of the Severi varieties over arbitrary fields. This can be regarded as a counterpart over arbitrary fields of the classification of smooth complex algebraic Severi varieties. The proofs just use projective geometry.
In the remaining time, I will discuss a geometric characterization of projective planes over quadratic alternative division algebras.
This talk is part of the Algebra Seminar series.
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