## Elliptic three-folds II: Multiple fibres

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- by Mark Gross PDF
- Trans. Amer. Math. Soc.
**349**(1997), 3409-3468 Request permission

## 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

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## Additional Information

**Mark Gross**- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 308804
- Email: mgross@math.cornell.edu
- 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 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**349**(1997), 3409-3468 - MSC (1991): Primary 14J30
- DOI: https://doi.org/10.1090/S0002-9947-97-01845-X
- MathSciNet review: 1401771