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Mat. Sb., 2007, Volume 198, Number 8, Pages 103–114 (Mi msb3665)  

This article is cited in 5 scientific papers (total in 5 papers)

$\mathbb Q$-factorial quartic threefolds

K. A. Shramov

M. V. Lomonosov Moscow State University

Abstract: It is proved that a nodal quartic threefold $X$ containing no planes is $\mathbb Q$-factorial if it has at most 12 singular points. An exception here is a quartic with precisely 12 singularities containing a quadric surface. Some geometric constructions relating to such a quartic are presented.
Bibliography: 14 titles.

DOI: https://doi.org/10.4213/sm3665

Full text: PDF file (494 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:8, 1165–1174

Bibliographic databases:

UDC: 512.76
MSC: Primary 14J30; Secondary 14E05, 14E07
Received: 07.09.2006 and 12.01.2007

Citation: K. A. Shramov, “$\mathbb Q$-factorial quartic threefolds”, Mat. Sb., 198:8 (2007), 103–114; Sb. Math., 198:8 (2007), 1165–1174

Citation in format AMSBIB
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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. K. A. Shramov, “Birational Rigidity and $\mathbb Q$-Factoriality of a Singular Double Cover of a Quadric Branched over a Divisor of Degree 4”, Math. Notes, 84:2 (2008), 280–289  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. A. Cheltsov, “On a conjecture of Ciliberto”, Sb. Math., 201:7 (2010), 1069–1090  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Alessio Corti, Mark Haskins, Johannes Nordström, Tommaso Pacini, “Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds”, Geom. Topol, 17:4 (2013), 1955  crossref  mathscinet  zmath  isi  scopus
    4. Kyusik Hong, “Nonrationality of nodal quartic threefolds”, Pacific J. Math, 266:1 (2013), 31  crossref  mathscinet  zmath  isi  scopus
    5. Cheltsov I., Grinenko M., “Birational Rigidity Is Not An Open Property”, Bull. Korean. Math. Soc., 54:5 (2017), 1485–1526  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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