The Fujiki class and positive degree maps

Gautam Bharali 1 , Indranil Biswas 1 ,  and Mahan Mj 1
  • 1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • 2 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • 3 Department of Mathematics, RKM Vivekananda University, P.O. Belur Math, Howrah 711202, India


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.

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