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Tohoku Mathematical Journal
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Article . 1987
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Tohoku Mathematical Journal
Article . 1987 . Peer-reviewed
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Infinitesimal deformations of generalized cusp singularities

Authors: Ogata, Shōetsu;

Infinitesimal deformations of generalized cusp singularities

Abstract

The paper is organized in three sections. In section 1 the author constructs a normal isolated singularity (V,p) having the property that \(V\setminus \{p\}\) is isomorphic to a quotient of a Siegel domain of the second kind. The author calls this singularity a ``cusp''. In section 2 he considers a singularity (V,p) which satisfied some additional condition in the sense of Thuchihashi. He shows that there exist isomorphisms \(T^ 1_ V \cong H^ 1(V\setminus \{p\},\theta_ V)\) and \(H^ 1(U,\theta_ U(-\log X)) \cong H^ 1(V\setminus \{p\},\theta_ V)\) for some resolution (U,X) of a ``cusp'' singularity (V,p) of a dimension greater than two. Section 3 contains the proofs. The paper is well written and contains complete bibliographic data on these results.

Related Organizations
Keywords

14B07, Deformations of complex singularities; vanishing cycles, Deformations of singularities, Siegel domain of the second kind, 32G11, cohomology group with compact support, 11F41, infinitesimal deformations of cusp singularities

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
hybrid