DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES

Abstract

In our previous work, we introduced a series of new derivation Lie algebras Lk(V) associated to an isolated hypersurface singularity (V,0). These are new analytic invariants of singularities. Here, we investigate L2(V) for fewnomial isolated singularities and obtain the formula of λk(V) (i.e., the dimension of Lk(V)) for trinomial singularities. Furthermore, we prove the sharp upper estimate conjecture for L2(V). This is a continuation of our previous work (Math. Z. 298:3-4 (2021), 1813–1829). We proposed two new conjectures for τk(V) and λk(V) and we prove these conjectures for a large class of singularities.