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Mosc. Math. J., 2012, Volume 12, Number 1, Pages 149–172 (Mi mmj451)  

This article is cited in 12 scientific papers (total in 12 papers)

Complex-analytic structures on moment-angle manifolds

Taras Panovabc, Yuri Ustinovskya

a Department of Mathematics and Mechanics, Moscow State University, Moscow, Russia,
b Institute for Information Transmission Problems, Russian Academy of Sciences
c Institute for Theoretical and Experimental Physics, Moscow, Russia,

Abstract: We show that the moment-angle manifolds corresponding to complete simplicial fans admit non-Kähler complex-analytic structures. This generalises the known construction of complex-analytic structures on polytopal moment-angle manifolds, coming from identifying them as LVM-manifolds. We proceed by describing Dolbeault cohomology and some Hodge numbers of moment-angle manifolds by applying the Borel spectral sequence to holomorphic principal bundles over toric varieties.

Key words and phrases: moment-angle manifold, simplicial fan, simple polytope, complex structure, Dolbeault cohomology, Hodge numbers.

DOI: https://doi.org/10.17323/1609-4514-2012-12-1-149-172

Full text: http://www.ams.org/.../abst12-1-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 32J18, 32L05, 32Q55, 57R19, 14M25
Received: September 3, 2010; in revised form March 1, 2011
Language:

Citation: Taras Panov, Yuri Ustinovsky, “Complex-analytic structures on moment-angle manifolds”, Mosc. Math. J., 12:1 (2012), 149–172

Citation in format AMSBIB
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\by Taras~Panov, Yuri~Ustinovsky
\paper Complex-analytic structures on moment-angle manifolds
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 149--172
\mathnet{http://mi.mathnet.ru/mmj451}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-149-172}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2952429}
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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. T. E. Panov, “Geometric structures on moment-angle manifolds”, Russian Math. Surveys, 68:3 (2013), 503–568  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Battisti L., “Lvmb Manifolds and Quotients of Toric Varieties”, Math. Z., 275:1-2 (2013), 549–568  crossref  mathscinet  zmath  isi  elib  scopus
    3. Yu. M. Ustinovsky, “Geometry of compact complex manifolds with maximal torus action”, Proc. Steklov Inst. Math., 286 (2014), 198–208  mathnet  crossref  crossref  isi  elib
    4. T. E. Panov, “On the cohomology of quotients of moment-angle manifolds”, Russian Math. Surveys, 70:4 (2015), 779–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Battaglia F., Zaffran D., “Foliations Modeling Nonrational Simplicial Toric Varieties”, Int. Math. Res. Notices, 2015, no. 22, 11785–11815  crossref  mathscinet  zmath  isi  elib  scopus
    6. Cai L., “Norm Minima in Certain Siegel Leaves”, Algebr. Geom. Topol., 15:1 (2015), 445–466  crossref  mathscinet  zmath  isi  elib  scopus
    7. Sorin Dumitrescu, Benjamin McKay, “Affine connections on complex manifolds of algebraic dimension zero”, Mosc. Math. J., 16:4 (2016), 675–689  mathnet  mathscinet
    8. T. Panov, Yu. Ustinovskiy, M. Verbitsky, “Complex geometry of moment-angle manifolds”, Math. Z., 284:1-2 (2016), 309–333  crossref  mathscinet  zmath  isi  scopus
    9. H. Ishida, “Torus invariant transverse Kahler foliations”, Trans. Am. Math. Soc., 369:7 (2017), 5137–5155  crossref  mathscinet  zmath  isi  scopus
    10. H. Park, “Wedge operations and doubling operations of real toric manifolds”, Chin. Ann. Math. Ser. B, 38:6 (2017), 1321–1334  crossref  mathscinet  zmath  isi  scopus
    11. L. Cai, “On products in a real moment-angle manifold”, J. Math. Soc. Jpn., 69:2 (2017), 503–528  crossref  mathscinet  zmath  isi  scopus
    12. Poddar M., Thakur A.S., “Group Actions, Non-Kahler Complex Manifolds and Skt Structures”, Complex Manifolds, 5:1 (2018), 9–25  crossref  mathscinet  zmath  isi  scopus
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