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Tytuł artykułu

The Fujiki class and positive degree maps

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-04-28
zaakceptowano
2015-02-24
online
2015-03-18
Twórcy
  • Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
autor
  • Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Bibliografia
  • [1] Abramovich D., Karu K., Matsuki K., Włodarczyk J., Torification and factorization of birational maps, Jour. Amer. Math. Soc.,2002, 15, 531–572
  • [2] Arapura D., Kähler solvmanifolds, Int. Math. Res. Not., 2004(3), 131–137[Crossref]
  • [3] Barlet D., How to use the cycle space in complex geometry, In: Several Complex Variables, Papers from the MSRI Programheld in Berkeley, CA, 1995–1996, Math. Sci. Res. Inst. Publ., 37, Cambridge University Press, Cambridge, 1999, 25–42
  • [4] Beauville A., Endomorphisms of hypersurfaces and other manifolds, Internat. Math. Res. Notices, 2001(1), 53–58
  • [5] Bharali G., Biswas I., Rigidity of holomorphic maps between fiber spaces, Internat. J. Math., 2014, 25(1), #145006, 8pp.[Crossref]
  • [6] Blanchard A., Sur les variétés analytiques complexes, Ann. Sci. Ecole Norm. Sup., 1956, 73, 157–202
  • [7] Carlson J.A., Toledo D., Harmonic mappings of Kähler manifolds to locally symmetric spaces, Inst. Hautes Etudes Sci. Publ.Math., 1989, 69, 173–201
  • [8] Fujiki A., Closedness of the Douady spaces of compact Kähler spaces, Publ. Res. Inst. Math. Sci., 1978/79, 14, 1–52[Crossref]
  • [9] Fujimoto Y., Endomorphisms of smooth projective 3-folds with non-negative Kodaira dimension, Publ. Res. Inst. Math. Sci.,2002, 38(1), 33–92
  • [10] Hironaka H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 1964, 79,109–326
  • [11] Hironaka H., Flattening theorem in complex-analytic geometry, Amer. Jour. Math., 1975, 97, 503–547
  • [12] Toledo D., personal communication, 2013
  • [13] Varouchas J., Stabilité de la classe des variétés Kähleriennes par certaines morphismes propres, Invent.Math., 1984, 77(1),117–127
  • [14] Varouchas J., Kähler spaces and proper open morphisms, Math. Ann., 1989, 283(1), 13–52
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_coma-2015-0002
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