Transactions of the American Mathematical Society

Author(s): Mark Gross
Journal: Trans. Amer. Math. Soc. 349 (1997), 3409-3468.
MSC (1991): Primary 14J30
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Abstract: Let $f:X\rightarrow S$ be an elliptic fibration with a section, where $S$

is a projective surface and $X$

is a projective threefold. We determine when it is possible to perform a logarithmic transformation along a closed subset $Z\subseteq S$ to obtain a new elliptic fibration $f':X'\rightarrow S$ which now has multiple fibres along $Z$

. This is done in the setting of Ogg-Shafarevich theory. We find a number of obstructions to performing such a logarithmic transformation, the very last of which takes values in the torsion part of the codimension 2 Chow group of $X$

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 14J30

Mark Gross
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: mgross@math.cornell.edu

DOI: 10.1090/S0002-9947-97-01845-X
PII: S 0002-9947(97)01845-X
Received by editor(s): June 19, 1995
Additional Notes: This material is based upon work supported by the North Atlantic Treaty Organization under a Grant awarded in 1990. Research at MSRI supported in part by NSF grant #DMS 9022140.
Copyright of article: Copyright 1997, American Mathematical Society

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