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Realization of Chern classes by subvarieties with certain singularities

Published online by Cambridge University Press:  22 January 2016

Hiroshi Morimoto
Hiroshi Morimoto*
Affiliation:
Nagoya University
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In this paper we are concerned with subvarieties which realize Chern classes of holomorphic vector bundles. The existence of these subvarieties is known in some cases (for instance, see A. Grotheridieck [2] for projective algebraic varieties and M. Cornalba and P. Griffiths [1] for Stein manifolds). In the present paper we realize Chern classes by subvarieties with singularities of a certain type. Our main theorem is as follows (see Def. 1.1.3 for the definition of quasilinear subvarieties).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 80 , December 1980 , pp. 49 - 74
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[ 1 ] Cornalba, M. and Griffiths, P., Analytic cycles and vector bundles on non-compact algebraic varieties, Inventiones Math., 28 (1975), 1–106.CrossRefGoogle Scholar
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[ 4 ] Whitney, H., Tangents to an analytic variety, Ann. Math., 81 (1965), 496–549.CrossRefGoogle Scholar
[ 5 ] Wu, W. T., Sur les classes charactéristiques des structures fibrées sphériques, Act. Sci. et Ind., n° 1183.Google Scholar