Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Elliptic three-folds II: Multiple fibres

Author: Mark Gross
Journal: Trans. Amer. Math. Soc. 349 (1997), 3409-3468
MSC (1991): Primary 14J30
MathSciNet review: 1401771
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $X$.

References [Enhancements On Off] (What's this?)

Similar Articles

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

Retrieve articles in all journals with MSC (1991): 14J30

Additional Information

Mark Gross
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853

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.
Article copyright: © Copyright 1997 American Mathematical Society