The Special Symplectic Structure of Binary Cubics

Marcus J. Slupinski () and Robert J. Stanton ()
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Marcus J. Slupinski: Université de Strasbourg (Strasbourg), IRMA
Robert J. Stanton: Ohio State University, Department of Mathematics

A chapter in Representation Theory, Complex Analysis, and Integral Geometry, 2012, pp 185-230 from Springer

Abstract: Abstract We present a thorough investigation of binary cubics over a field of characteristic not 2 or 3 using equivariant symplectic methods. The primary symplectic tools are the moment map and its norm, as well as the symplectic gradient of the norm. Among the results obtained are a symplectic stratification of the space of binary cubics, the identification of a group structure on generic orbits, a symplectic derivation of the Cardano-Tartaglia formula, and a symplectic formulation and proof of the Eisenstein syzygy.

Keywords: Moment map; Binary cubic polynomials; Special symplectic structure; Prehomogeneous vector space (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4817-6_8

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DOI: 10.1007/978-0-8176-4817-6_8

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