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Hodge theory for twisted differentials

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EN
Abstrakty
EN
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
1
Opis fizyczny
Daty
otrzymano
2014-08-22
zaakceptowano
2014-11-09
online
2014-11-29
Twórcy
  • Istituto Nazionale di Alta Matematica
    (Current address) Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124, Parma,
    Italy
  • Department of Mathematics, Tokyo Institute of Technology, 1-12- 1-H-7, O-okayama,
    Meguro, Tokyo 152-8551, Japan, kasuya@math.titech.ac.jp
Bibliografia
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  • [4] D. Angella, H. Kasuya, Bott-Chern cohomology of solvmanifolds, arXiv:1212.5708v3
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  • [7] D. Arapura, Kähler solvmanifolds, Int. Math. Res. Not. 2004 (2004), no. 3, 131–137.
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  • [math.GT].
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  • [18] A. Fujiki, On automorphism groups of compact Kähler manifolds, Invent. Math. 44 (1978), no. 3, 225–258.[Crossref]
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  • [20] K. Hasegawa, A note on compact solvmanifolds with Kähler structures, Osaka J. Math. 43 (2006), no. 1, 131–135.
  • [21] H. Kasuya, Techniques of computations of Dolbeault cohomology of solvmanifolds, Math. Z. 273 (2013), no. 1-2, 437–447.[WoS]
  • [22] H. Kasuya, Hodge symmetry and decomposition on non-Kähler solvmanifolds, J. Geom. Phys. 76 (2014), 61–65.
  • [23] H. Kasuya, Flat bundles and Hyper-Hodge decomposition on solvmanifolds, arXiv:1309.4264v1
  • [math.DG], To appear inInt. Math. Res. Not. IMRN.
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  • [26] B. G. Moˇıšezon, On n-dimensional compact complexmanifolds having n algebraically independent meromorphic functions.I, II, III, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), no. 1–2–3, 133–174, 345–386, 621–656. Translation in Am. Math. Soc.,Transl., II. Ser. 63 (1967), 51–177.
  • [27] I. Nakamura, Complex parallelisable manifolds and their small deformations, J. Differ. Geom. 10 (1975), no. 1, 85–112.
  • [28] L. Ornea, M. Verbitsky, Morse-Novikov cohomology of locally conformally Kählermanifolds, J. Geom. Phys. 59 (2009), no. 3,295–305.[Crossref]
  • [29] I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), no. 6, 359–363.[Crossref]
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  • [math.AG].
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  • [34] R O., Wells, Jr., Differential analysis on complex manifolds, Third edition,With a new appendix by Oscar Garcia-Prada, GraduateTexts in Mathematics, 65, Springer, New York, 2008.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_coma-2014-0005
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