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 Tr. Mat. Inst. Steklova, 2012, Volume 279, Pages 269–287 (Mi tm3432)

This article is cited in 3 scientific papers (total in 3 papers)

Bochner–Hartogs type extension theorem for roots and logarithms of holomorphic line bundles

S. Ivashkovichab

a Université Lille-1, UFR de Mathématiques, Villeneuve d'Ascq, France
b Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, L'viv, Ukrain

Abstract: We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when the dimension and Morse index of a critical point is 2. In that case we give an explicit description of obstructions to the extension.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 279, 257–275

Bibliographic databases:

UDC: 517.55
Received in April 2011
Language:

Citation: S. Ivashkovich, “Bochner–Hartogs type extension theorem for roots and logarithms of holomorphic line bundles”, Analytic and geometric issues of complex analysis, Collected papers, Tr. Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, Moscow, 2012, 269–287; Proc. Steklov Inst. Math., 279 (2012), 257–275

Citation in format AMSBIB
\Bibitem{Iva12} \by S.~Ivashkovich \paper Bochner--Hartogs type extension theorem for roots and logarithms of holomorphic line bundles \inbook Analytic and geometric issues of complex analysis \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2012 \vol 279 \pages 269--287 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3432} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3086770} \elib{https://elibrary.ru/item.asp?id=18447462} \transl \jour Proc. Steklov Inst. Math. \yr 2012 \vol 279 \pages 257--275 \crossref{https://doi.org/10.1134/S0081543812080184} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314063000018} 

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This publication is cited in the following articles:
1. R. B. Andrist, N. Shcherbina, E. F. Wold, “The Hartogs extension theorem for holomorphic vector bundles and sprays”, Ark. Mat., 54:2 (2016), 299–319
2. C. Canales Gonzalez, “Levi-flat hypersurfaces and their complement in complex surfaces”, Ann. Inst. Fourier, 67:6 (2017), 2423–2462
3. Zh. Chen, “A counterexample to Hartogs' type extension of holomorphic line bundles”, J. Geom. Anal., 28:3 (2018), 2624–2643
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