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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2019, Volume 305, Pages 271–282 (Mi tm4013)  

The Smooth Torus Orbit Closures in the Grassmannians

Masashi Noji, Kazuaki Ogiwara

Division of Mathematics & Physics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Abstract: It is known that for the natural algebraic torus actions on the Grassmannians, the closures of torus orbits are normal and hence are toric varieties, and that these toric varieties are smooth if and only if the corresponding matroid polytopes are simple. We prove that simple matroid polytopes are products of simplices and that smooth torus orbit closures in the Grassmannians are products of complex projective spaces. Moreover, it turns out that the smooth torus orbit closures are uniquely determined by the corresponding simple matroid polytopes.

Funding Agency Grant Number
Russian Foundation for Basic Research
The authors were partially supported by the bilateral program “Topology and Geometry of Torus Actions, Cohomological Rigidity, and Hyperbolic Manifolds” between JSPS and RFBR.


DOI: https://doi.org/10.4213/tm4013

Full text: PDF file (236 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 305, 251–261

Bibliographic databases:

UDC: 519.1
MSC: Primary: 14M25; Secondary: 14M15, 05C99
Received: December 11, 2018
Revised: January 10, 2019
Accepted: March 14, 2019

Citation: Masashi Noji, Kazuaki Ogiwara, “The Smooth Torus Orbit Closures in the Grassmannians”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Tr. Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 271–282; Proc. Steklov Inst. Math., 305 (2019), 251–261

Citation in format AMSBIB
\Bibitem{NojOgi19}
\by Masashi~Noji, Kazuaki~Ogiwara
\paper The Smooth Torus Orbit Closures in the Grassmannians
\inbook Algebraic topology, combinatorics, and mathematical physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 305
\pages 271--282
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4013}
\crossref{https://doi.org/10.4213/tm4013}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 305
\pages 251--261
\crossref{https://doi.org/10.1134/S0081543819030143}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000491421700014}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85073525123}


Linking options:
  • http://mi.mathnet.ru/eng/tm4013
  • https://doi.org/10.4213/tm4013
  • http://mi.mathnet.ru/eng/tm/v305/p271

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:61
    References:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019