Classification of linear actions of algebraic groups on spaces of homogeneous forms (Q416952)

The paper is devoted to the study of orbits of an algebraic group \(G\) acting on the space of rational forms in many variables by linear changes of coordinates. The main result of the paper consists in finding the field of differential invariants of such an action and obtaining an effective criterion for distinguishing between the orbits of forms with nonzero Hessian. In other words, the authors present a method for classifying the \(G\)-orbits of regular rational forms of any degree. Surprisingly, the obtained classification depends neither on the degree \(n\), on the number \(p\) of variables, nor even in any sense on the group \(G\).