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

Abstract

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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Complex Manifolds is a fully peer-reviewed, open access electronic journal that publishes cutting-edge research on complex manifolds and related results from differential geometry, algebraic geometry and complex analysis. The journal focuses on complex geometry from the differential, algebraic and analytical point of view, and is a forum where all the aspects of these problems can be discussed.

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