Extendability of differential forms on non-isolated singularities. (English) Zbl 0658.14009

In these decades Hodge theory has been extended to the germs of isolated singular points of complex spaces by several people, and continuation theorems for holomorphic differential forms across exceptional sets have been known as application.
This article first gives a nice survey on this topic, collecting the results obtained by D. v. Straten and J. Steenbrink [Abh. Math. Semin. Univ. Hamburg 55, 97-109 (1985; Zbl 0584.32018)’), V. Navarro Aznar [Systèmes différentiels et singularités, Colloq. Luminý, Astérisque 130, 272-307 (1985; Zbl 0599.14007)], Kersken (Habilitationsschrift, Bochum 1987) and the reviewer [Publ. Res. Inst. Math. Sci. 24, No.2, 253-263 (1988; Zbl 0653.32012)], and extend them to the germs of non-isolated singular points. The result has an immediate application to the well known problem of Zariski and Lipman, as the author remarks in the introduction. The idea of the proof is very natural, but the reader is required to be acquaintd with basic techniques in algebraic geometry.
Reviewer: T.Ohsawa


14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
32D15 Continuation of analytic objects in several complex variables
14B05 Singularities in algebraic geometry
32B10 Germs of analytic sets, local parametrization
32S45 Modifications; resolution of singularities (complex-analytic aspects)
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