Projective classification of binary and ternary forms

Global Lie–Tresse theorem

“…If we restrict to Y ≡ 0, this becomes the well-studied example by S. Lie, A. Tresse and A. Kumpera [29]. This example is rather simple 7 : there is only one singular orbit {u = 0} and the algebra of invariants is generated by 1 differential invariant and two invariant derivations.…”

“…It is important to use global invariants (as algebraic classifications are always global). In this way the classical equivalence problem for binary and ternary forms was solved in [7], and a more general problem on equivalence under an irreducible algebraic action of a reductive Lie group can be also solved.…”

“…This implies, in particular, a possibility to solve algebraic equivalence problems via the differential-geometric technique (see, e.g., [7]). …”

On affine classification of functions and foliations on the plane

“…We define corresponding symmetric total differential d s Γ on the jet space. Therefore we have (see [4])…”

“…We will use constructions described in [4]. First of all we note that we consider only such functions f , that F (f ) ≡ 0.…”