Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Matematicheskie Zametki, 2009, Volume 85, Issue 5, Pages 643–651
DOI: https://doi.org/10.4213/mzm6907 (Mi mzm6907) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the Factoriality of Cox rings

I. V. Arzhantsev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (474 kB) Citations (12)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm6907
Abstract: The generalized Cox construction associates with an algebraic variety a remarkable invariant — its total coordinate ring, or Cox ring. In this note, we give a new proof of the factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on the notion of graded factoriality. We show that if the divisor class group has torsion, then the Cox ring is again factorially graded, but factoriality may be lost.
Keywords: total coordinate ring, Cox ring, algebraic variety, factorial ring, graded factoriality, divisor class group, torsion, Weil divisor, Cartier divisor.
Received: 05.02.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 5, Pages 623–629
DOI: https://doi.org/10.1134/S0001434609050022
Bibliographic databases:
UDC: 512.71
Language: Russian
Citation: I. V. Arzhantsev, “On the Factoriality of Cox rings”, Mat. Zametki, 85:5 (2009), 643–651; Math. Notes, 85:5 (2009), 623–629
Citation in format AMSBIB
\Bibitem{Arz09}
\by I.~V.~Arzhantsev
\paper On the Factoriality of Cox rings
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 5
\pages 643--651
\mathnet{http://mi.mathnet.ru/mzm6907}
\crossref{https://doi.org/10.4213/mzm6907}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2572855}
\zmath{https://zbmath.org/?q=an:1192.14008}
\elib{https://elibrary.ru/item.asp?id=15301154}
\transl
\jour Math. Notes
\yr 2009
\vol 85
\issue 5
\pages 623--629
\crossref{https://doi.org/10.1134/S0001434609050022}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267684500002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69949122944}
Linking options:
  • https://www.mathnet.ru/eng/mzm6907
  • https://doi.org/10.4213/mzm6907
  • https://www.mathnet.ru/eng/mzm/v85/i5/p643
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024