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Sbornik: Mathematics, 2000, Volume 191, Issue 9, Pages 1399–1419
DOI: https://doi.org/10.1070/sm2000v191n09ABEH000511 (Mi sm511) 		 
This article is cited in 29 scientific papers (total in 29 papers)

On a smooth quintic 4-fold

I. A. Cheltsov
English version PDF (230 kB) Citations (29)
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DOI: https://doi.org/10.1070/sm2000v191n09ABEH000511
Abstract: The birational geometry of an arbitrary smooth quintic 4-fold is studied using the properties of log pairs. As a result, a new proof of its birational rigidity is given and all birational maps of a smooth quintic 4-fold into fibrations with general fibre of Kodaira dimension zero are described.
In the Addendum similar results are obtained for all smooth hypersurfaces of degree $n$ in $\mathbb P^n$ in the case of $n$ equal to 6, 7, or 8.
Received: 10.06.1999 and 19.01.2000
Russian version:
Matematicheskii Sbornik, 2000, Volume 191, Number 9, Pages 139–160
DOI: https://doi.org/10.4213/sm511
Bibliographic databases:
UDC: 513.6
MSC: 14J35, 14E05
Language: English
Original paper language: Russian
Citation: I. A. Cheltsov, “On a smooth quintic 4-fold”, Mat. Sb., 191:9 (2000), 139–160; Sb. Math., 191:9 (2000), 1399–1419
Citation in format AMSBIB
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\paper On a smooth quintic 4-fold
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\pages 139--160
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  • https://www.mathnet.ru/eng/sm/v191/i9/p139
    • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    English version PDF:8
    References:51
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