Let $(\sM,\sL)$ be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface $S\in|\sL|$ is studied. This problem was previously considered and partially solved by the first and fourth author, who gave a satisfactory classification unless $h^1(\sO_\sM)=0$ and $p_g(S)=3,4,5$. This paper focuses on the remaining cases which are the hardest, settling the problem.
On the birationality of the bicanonical map of a surface section of a threefold
BELTRAMETTI, MAURO CARLO;
2007-01-01
Abstract
Let $(\sM,\sL)$ be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface $S\in|\sL|$ is studied. This problem was previously considered and partially solved by the first and fourth author, who gave a satisfactory classification unless $h^1(\sO_\sM)=0$ and $p_g(S)=3,4,5$. This paper focuses on the remaining cases which are the hardest, settling the problem.
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