Resumen de Maximal multihomogeneity of algebraic hypersurface singularities

Mathias Schulze

• From the degree zero part of the logarithmic vector fields along analgebraic hypersurface singularity we identify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one-to-one correspondence to maximal tori in the linear jet of the embedded automorphism group. These results are motivated by Kyoji Saito's characterization of quasihomogeneity for isolated hypersurface singularities [Saito in Invent. Math. 14, 123-142 (1971)] and extend previous work with Granger and Schulze [Compos. Math. 142(3), 765-778 (2006), Theorem 5.4] and of Hauser and Müller [Nagoya Math. J. 113, 181-186 (1989), Theorem 4].