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Depth and differential forms. (English) Zbl 1105.14021
Lossen, Christoph (ed.) et al., Singularities and computer algebra. Selected papers of the conference, Kaiserslautern, Germany, October 18–20, 2004 on the occasion of Gert-Martin Greuel’s 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-68309-2/pbk). London Mathematical Society Lecture Note Series 324, 211-232 (2006).
The author shows that many major theorems valid for smooth complex projective varieties (such as Hodge decomposition, Lefschetz theorem on hyperplane section, Akizuki-Nakano theorem) remain valid to some extent when we deal with projective varieties that are locally complete intersections.
For the entire collection see [Zbl 1086.14001].
14F40 de Rham cohomology and algebraic geometry
14M10 Complete intersections
32S20 Global theory of complex singularities; cohomological properties
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
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