Via the XJC correspondence proved in [21] we provide some structure theorems for quadro-quadric Cremona transformations and for extremal varieties 3-covered by twisted cubics by reinterpreting for these objects the algebraic results on the solvability of the radical of Jordan algebras. In this way we can define the semi-simple part and the radical part of a quadro-quadric Cremona transformation, respectively of an extremal variety 3-covered by twisted cubics, and then describe how general objects are constructed from the semi simple ones, which are completely classified modulo certain equivalences, via suitable null radical extensions.

Quadro-quadric Cremona maps and varieties 3-connected by cubics: semi-simple part and radical

RUSSO, Francesco
2013

Abstract

Via the XJC correspondence proved in [21] we provide some structure theorems for quadro-quadric Cremona transformations and for extremal varieties 3-covered by twisted cubics by reinterpreting for these objects the algebraic results on the solvability of the radical of Jordan algebras. In this way we can define the semi-simple part and the radical part of a quadro-quadric Cremona transformation, respectively of an extremal variety 3-covered by twisted cubics, and then describe how general objects are constructed from the semi simple ones, which are completely classified modulo certain equivalences, via suitable null radical extensions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/15761
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