## Fibered threefolds and Lang-Vojta’s conjecture over function fields

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- by Amos Turchet PDF
- Trans. Amer. Math. Soc.
**369**(2017), 8537-8558 Request permission

## Abstract:

Using the techniques introduced by Corvaja and Zannier in 2008 we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane. In this situation we deal with sections of an affine threefold fibered over a curve, whose boundary, in the natural projective completion, is a quartic bundle over the base whose fibers have three irreducible components. We prove that the image of each section has bounded degree in terms of the Euler characteristic of the base curve.## References

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## Additional Information

**Amos Turchet**- Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden
- Address at time of publication: Department of Mathematics, University of Washington, Seattle, Washington 98195
- ORCID: 0000-0003-3411-2521
- Email: aturchet@uw.edu
- Received by editor(s): July 2, 2015
- Received by editor(s) in revised form: January 26, 2016
- Published electronically: May 30, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 8537-8558 - MSC (2010): Primary 14G40; Secondary 11G50
- DOI: https://doi.org/10.1090/tran/6968
- MathSciNet review: 3710634