On projective threefolds of general type with small positive geometric genus

  • Received: 01 April 2020 Revised: 01 October 2020 Published: 24 November 2020
  • Primary: 14J30, 14E05; Secondary: 14E30, 14B05

  • In this paper we study the pluricanonical maps of minimal projective 3-folds of general type with geometric genus $ 1 $, $ 2 $ and $ 3 $. We go in the direction pioneered by Enriques and Bombieri, and other authors, pinning down, for low projective genus, a finite list of exceptions to the birationality of some pluricanonical map. In particular, apart from a finite list of weighted baskets, we prove the birationality of $ \varphi_{16} $, $ \varphi_{6} $ and $ \varphi_{5} $ respectively.

    Citation: Meng Chen, Yong Hu, Matteo Penegini. On projective threefolds of general type with small positive geometric genus[J]. Electronic Research Archive, 2021, 29(3): 2293-2323. doi: 10.3934/era.2020117

    Related Papers:

  • In this paper we study the pluricanonical maps of minimal projective 3-folds of general type with geometric genus $ 1 $, $ 2 $ and $ 3 $. We go in the direction pioneered by Enriques and Bombieri, and other authors, pinning down, for low projective genus, a finite list of exceptions to the birationality of some pluricanonical map. In particular, apart from a finite list of weighted baskets, we prove the birationality of $ \varphi_{16} $, $ \varphi_{6} $ and $ \varphi_{5} $ respectively.



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