JournalsprimsVol. 41, No. 1pp. 1–10

Algebraic Local Cohomology Classes Attached to Quasi-Homogeneous Hypersurface Isolated Singularities

  • Shinichi Tajima

    University of Tsukuba, Ibaraki, Japan
  • Yayoi Nakamura

    Kinki University, Osaka, Japan
Algebraic Local Cohomology Classes Attached to Quasi-Homogeneous Hypersurface Isolated Singularities cover
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Abstract

The purpose of this paper is to study hypersurface isolated singularities by using partial differential operators based on em>D-modules theory. Algebraic local cohomology classes supported at a singular point that constitute the dual space of the Milnor algebra are considered. It is shown that an isolated singularity is quasi-homogeneous if and only if an algebraic local cohomology class generating the dual space can be characterized as a solution of a holonomic system of first order partial differential equations.

Cite this article

Shinichi Tajima, Yayoi Nakamura, Algebraic Local Cohomology Classes Attached to Quasi-Homogeneous Hypersurface Isolated Singularities. Publ. Res. Inst. Math. Sci. 41 (2005), no. 1, pp. 1–10

DOI 10.2977/PRIMS/1145475402