JournalsrsmupVol. 125pp. 15–38

Examples of Threefolds with Kodaira Dimension 1 or 2

  • Alberto Calabri

    Università di Ferrara, Italy
  • Masaaki Murakami

    Universität Bayreuth, Germany
  • Ezio Stagnaro

    Università di Padova, Italy
Examples of Threefolds with Kodaira Dimension 1 or 2 cover
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Abstract

We construct three nonsingular threefolds XX, XX' and XX'' with vanishing irregularities. XX has Kodaira dimension == κ(X)=1\kappa(X)=1 and its mm-canonical transformation φmKX\varphi_{|mK_X|} has the following property\,: the minimum integer number m0m_0, such that the dimension of the image dim φmKX(X)\varphi_{|mK_X|}(X) == κ(X)\kappa(X) == 11 for mm0m \geq m_0, is given by m0=32m_0=32. XX' and XX'' have Kodaira dimension κ(X)=κ(X)=2\kappa(X')=\kappa(X'')=2 and their mm-canonical transformations have the properties\,: dim φmKX(X)\varphi_{|mK_{X'}|}(X') == κ(X)\kappa(X') == 22 if and only if m12m \geq 12, dim φmKX(X)\varphi_{|mK_{X''}|}(X'') == κ(X)\kappa(X'') == 22 if and only if m=9,10m = 9, 10 or m12m \geq 12.

Cite this article

Alberto Calabri, Masaaki Murakami, Ezio Stagnaro, Examples of Threefolds with Kodaira Dimension 1 or 2. Rend. Sem. Mat. Univ. Padova 125 (2011), pp. 15–38

DOI 10.4171/RSMUP/125-2