Publications of the Research Institute for Mathematical Sciences


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Volume 41, Issue 1, 2005, pp. 1–10
DOI: 10.2977/prims/1145475402

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

Shinichi Tajima[1] and Yayoi Nakamura[2]

(1) Graduate School of Pure and Applied Sciences, University of Tsukuba, Tenodai 1-1-1, Tsukuba, 305-8571, IBARAKI, JAPAN
(2) School of Science and Engineering, Kinki University, 3-4-1, Kowakae, Higashiosaka, 577-8502, OSAKA, JAPAN

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.

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Tajima Shinichi, Nakamura Yayoi: Algebraic Local Cohomology Classes Attached to Quasi-Homogeneous Hypersurface Isolated Singularities. Publ. Res. Inst. Math. Sci. 41 (2005), 1-10. doi: 10.2977/prims/1145475402