An inequality conjecture and a weak Torelli-type theorem for isolated complete intersection singularities

Abstract

In this paper, we propose an inequality conjecture for the dimensions of derivation Lie algebras associated to isolated complete intersection singularities. We verify this conjecture for simple and unimodal isolated complete intersection singularities. We also construct several new one-parameter families of solvable Lie algebras from T10, R9, U11, V10, Y11, and M11 singularities and show that the weak Torelli-type theorem holds.