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

Examples of threefolds with Kodaira dimension 1 or 2

Abstract

We construct three nonsingular threefolds X, X' and X''. X has Kodaira dimension = \kappa(X)=1 and its m-canonical transformation \varphi_{|mK_X|} has the following property: the minimum integer number m_0, such that the dimension of the image dim \varphi_{|mK_X|}(X) = \kappa(X) = 1 for m \geq m_0, it is given by m_0=32. X' and X'' have Kodaira dimension \kappa(X')=\kappa(X'')=2 and their m-canonical transformations have the properties: dim \varphi_{|mK_{X'}|}(X') = \kappa(X') = 2 if and only if m \geq 12, dim \varphi_{|mK_{X''}|}(X'') = \kappa(X'') = 2 if and only if m = 9, 10 or m \geq 12.
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2011
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/101627
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