Invariants of Binary Forms

Vishwanath Krishnamoorthy, Tanush Shaska, Helmut Voelklein

Published 2012-09-03Version 1

Basic invariants of binary forms over $\mathbb C$ up to degree 6 (and lower degrees) were constructed by Clebsch and Bolza in the 19-th century using complicated symbolic calculations. Igusa extended this to algebraically closed fields of any characteristic using difficult techniques of algebraic geometry. In this paper a simple proof is supplied that works in characteristic $p > 5$ and uses some concepts of invariant theory developed by Hilbert (in characteristic 0) and Mumford, Haboush et al. in positive characteristic. Further the analogue for pairs of binary cubics is also treated.