Cubic hyper-equisingular families of complex projective varieties. I. (English) Zbl 0852.32022
The author studies so-called cubic hyper-equisingular families of complex projective varieties to understand and describe the variation of mixed Hodge structure, which comes from a locally trivial family of projective varieties with ordinary singularities.
In this first part, one finds definitions and cohomological descent.
[For part II see ibid., 210-212 (1995; see the following review)].
In this first part, one finds definitions and cohomological descent.
[For part II see ibid., 210-212 (1995; see the following review)].
Reviewer: G.Pfister (Kaiserslautern)
MSC:
| 32S35 | Mixed Hodge theory of singular varieties (complex-analytic aspects) |
| 32S15 | Equisingularity (topological and analytic) |
| 14D07 | Variation of Hodge structures (algebro-geometric aspects) |
Keywords:
mixed Hodge structures; equisingular family; variation; variation of mixed Hodge structure; infinitesimal period mapCitations:
Zbl 0852.32023References:
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| [2] | R. Hartshorne: On the de Rham cohomology of algebraic varieties. Publ. Math. IHES, 45, 5-99 (1976). · Zbl 0326.14004 · doi:10.1007/BF02684298 |
| [3] | S. Tsuboi: Deformations of locally stable holo-morphic maps and locally trivial displacements of analytic subvarieties with ordinary singularities. Sci. Rep. Kagoshima Univ., 35, 9-90 (1986). · Zbl 0608.32006 |
| [4] | S. Tsuboi: Global existence of the universal locally trivial family of analytic subvarieties with locally stable parametrizations of a compact complex manifold. J. Fac. Sci. Univ. Tokyo, 40, no.l, 161-201 (1993). · Zbl 0790.32021 |
| [5] | S. Tsuboi : Variations of mixed Hodge structure arising from cubic hyperequisingular families of complex projective varieties. I. II (Preprint series no.22, no.23, Institute of Mathematics, University of Oslo, 1995). |
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