Maximal multihomogeneity of algebraic hypersurface singularities

• Autores: Mathias Schulze
• Localización: Manuscripta mathematica, ISSN 0025-2611, Vol. 123, Nº. 4, 2007, págs. 373-379
• Idioma: inglés
• DOI: 10.1007/s00229-007-0104-4
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• Resumen

  • 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].