On the Birationality of the Bicanonical Map of a Surface Section of a Threefold |
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| Authors: | M. C. Beltrametti C. Ciliberto A. Lanteri A. J. Sommese |
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| Affiliation: | 1. Department of Mathematics , University of Genova , Genova, Italy beltrame@dima.unige.it;3. Department of Mathematics , Second University of Rome “Tor Vergata” , Rome, Italy;4. Department of Mathematics “F. Enriques” , University of Milan , Milan, Italy;5. Department of Mathematics , University of Notre Dame , Notre Dame, Indiana, USA |
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| Abstract: | Let (?, ?) be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface S ∈ |?| is studied. This problem was previously considered and partially solved by the first and fourth author, who gave a satisfactory classification unless h1(𝒪?) = 0 and pg(S) = 3, 4, 5. This article focuses on the remaining cases which are the hardest, settling the problem. |
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| Keywords: | Adjunction theory Bicanonical map Log-general type Smooth complex polarized threefold Surface section Surface of general type Very ample line bundle |
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