Quadratic Involutions on Binary Forms

Details Quadratic Involutions on Binary Forms Quadratic Involutions on Binary Forms

2010-08-18

arxiv.org/abs/1008.3117v2

Mathematics

Algebraic Geometry

47 pages, 46 figures, minor typos fixed

Scientific paper

There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using compound transvectant formulae. We also study the associated varieties of forms which are preserved by such involutions. Along the way we prove a recoupling formula for transvectants, which is used to deduce a system of equations satisfied by the coefficients in these involutions.

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