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Mat. Sb., 2006, Volume 197, Number 3, Pages 87–116 (Mi msb1536)  

This article is cited in 4 scientific papers (total in 4 papers)

Factoriality of nodal three-dimensional varieties and connectedness of the locus of log canonical singularities

I. A. Cheltsov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Shokurov's vanishing theorem is used for the proof of the $\mathbb Q$-factoriality of the following nodal threefolds: a complete intersection of hypersurfaces $F$ and $G$ in $\mathbb P^5$ of degrees $n$ and $k$, $n\geqslant k$, such that $G$ is smooth and $|{\operatorname{Sing}(F\cap G)}|\leqslant(n+k-2)(n-1)/5$; a double cover of a smooth hypersurface $F\subset\mathbb P^4$ of degree $n$ branched over the surface cut on $F$ by a hypersurface $G\subset\mathbb P^4$ of degree $2r\geqslant n$, provided that $|{\operatorname{Sing}(F\cap G)}|\leqslant(2r+n-2)r/4$.
Bibliography: 71 titles.

DOI: https://doi.org/10.4213/sm1536

Full text: PDF file (707 kB)
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English version:
Sbornik: Mathematics, 2006, 197:3, 387–414

Bibliographic databases:

UDC: 512.76
MSC: 14J17, 14J30
Received: 08.02.2005

Citation: I. A. Cheltsov, “Factoriality of nodal three-dimensional varieties and connectedness of the locus of log canonical singularities”, Mat. Sb., 197:3 (2006), 87–116; Sb. Math., 197:3 (2006), 387–414

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math., 264 (2009), 102–109  mathnet  crossref  mathscinet  isi  elib
    2. SŁAWOMIR CYNK, SŁAWOMIR RAMS, “NON-FACTORIAL NODAL COMPLETE INTERSECTION THREEFOLDS”, Commun. Contemp. Math, 2012, 1250064  crossref  mathscinet  isi  scopus
    3. Cynk S., Rams S., “On Calabi-Yau Threefolds Associated To a Web of Quadrics”, Forum Math., 27:2 (2015), 699–734  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. V. Pukhlikov, “Factorial hypersurfaces”, Proc. Steklov Inst. Math., 299 (2017), 205–218  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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