Quadratic Involutions on Binary Forms

2010/08/18 by Abdelmalek Abdesselam, Abdesselam, Abdelmalek, Jaydeep Chipalkatti +1
Mathematics · #13A50 #22E70 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:13A50 #msc:22E70

paper · pdf · doi:10.48550/arxiv.1008.3117

Typos in formula of Proposition 7.1 fixed

arxiv created 2019/03/21 · arxiv updated 2019/03/25

Abstract

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.

Related

• Binary quadratic forms: modern developments
• Reduction theory of binary forms
• Counting Square Discriminants
• Associated forms of binary quartics and ternary cubics
• Varieties of Sums of Powers for binary forms