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 Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 5, Pages 1008–1036 (Mi izv2145)

Tensor differential forms on algebraic varieties

P. Bryukman

Abstract: Tensor (differential) forms on projective varieties are defined and studied in connection with certain birational invariants.
A sufficiently complete picture of the set of all tensor forms of the first kind on smooth projective hypersurfaces is given.
Restrictions of tensor forms, given on any smooth projective variety, to its intersection with a hypersurface are investigated. In particular, an analog of Lefschetz's theorem involving the usual skew-symmetric form is proved.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:5, 1021–1048

Bibliographic databases:

UDC: 513.66
MSC: Primary 14A10; Secondary 14F10

Citation: P. Bryukman, “Tensor differential forms on algebraic varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 35:5 (1971), 1008–1036; Math. USSR-Izv., 5:5 (1971), 1021–1048

Citation in format AMSBIB
\Bibitem{Bry71} \by P.~Bryukman \paper Tensor differential forms on algebraic varieties \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1971 \vol 35 \issue 5 \pages 1008--1036 \mathnet{http://mi.mathnet.ru/izv2145} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=292844} \zmath{https://zbmath.org/?q=an:0221.14012} \transl \jour Math. USSR-Izv. \yr 1971 \vol 5 \issue 5 \pages 1021--1048 \crossref{https://doi.org/10.1070/IM1971v005n05ABEH001199} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. F. A. Bogomolov, “Holomorphic tensors and vector bundles on projective varieties”, Math. USSR-Izv., 13:3 (1979), 499–555
2. F. A. Bogomolov, “Holomorphic symmetric tensors on projective surfaces”, Russian Math. Surveys, 33:5 (1978), 179–180
3. D. A. Rumynin, “Lie algebras in symmetric monoidal categories”, Siberian Math. J., 54:5 (2013), 905–921
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