Title: The geometric classification of Leibniz algebras,
Abstract: We describe all rigid algebras and all irreducible components in the variety
of four dimensional Leibniz algebras $\mathfrak{Leib}_4$ over $\mathbb{C}.$ In
particular, we prove that the Grunewald--O'Halloran conjecture is not valid and
the Vergne conjecture is valid for $\mathfrak{Leib}_4.$