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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 305, Pages 271–282
DOI: https://doi.org/10.4213/tm4013 (Mi tm4013) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (236 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4013
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.
Keywords: Toric variety, Grassmannian, torus orbit closure, matroid polytope, bipartite graph.
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.
Received: December 11, 2018
Revised: January 10, 2019
Accepted: March 14, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 305, Pages 251–261
DOI: https://doi.org/10.1134/S0081543819030143
Bibliographic databases:
Document Type: Article
UDC: 519.1
MSC: Primary: 14M25; Secondary: 14M15, 05C99
Language: Russian
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, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 271–282; Proc. Steklov Inst. Math., 305 (2019), 251–261
Citation in format AMSBIB
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\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 Trudy Mat. Inst. Steklova
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\vol 305
\pages 271--282
\publ Steklov Math. Inst. RAS
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    • This publication is cited in the following 2 articles:
    1. Victor M. Buchstaber, Svjetlana Terzić, Fields Institute Communications, 89, Toric Topology and Polyhedral Products, 2024, 81  crossref
    2. V. M. Buchstaber, S. Terzić, “Resolution of Singularities of the Orbit Spaces $G_{n,2}/T^n$”, Proc. Steklov Inst. Math., 317 (2022), 21–54  mathnet  crossref  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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