| 1. |
- Ascher, K., et al.
(author)
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A fibered power theorem for pairs of log general type
- 2016
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In: Algebra & Number Theory. - : Mathematical Sciences Publishers. - 1937-0652 .- 1944-7833. ; 10:7, s. 1581-1600
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Journal article (peer-reviewed)abstract
- Let f : (X, D) -> B be a stable family with log canonical general fiber. We prove that, after a birational modification of the base (B) over tilde -> B, there is a morphism from a high fibered power of the family to a pair of log general type. If in addition the general fiber is openly canonical, then there is a morphism from a high fibered power of the original family to a pair openly of log general type.
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| 2. |
- Das, Pranabesh, et al.
(author)
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Invitation to integral and rational points on curves and surfaces
- 2015
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In: Contemporary Mathematics. - Providence, Rhode Island : American Mathematical Society. - 1098-3627 .- 0271-4132. ; 654, s. 53-73
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Conference paper (peer-reviewed)abstract
- We provide a basic short introduction to Diophantine Geometry focusing on solutions to polynomial equations that correspond to rational and integral point of curves and surfaces. The methods employed are quite elementary and require no advanced background. We provide several explicit examples as well as ample citation for the motivated reader, aiming at introducing non-specialist to this intriguing world.
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| 3. |
- Turchet, Amos, 1984
(author)
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Fibered threefolds and Lang-Vojta’s conjecture over function fields
- 2017
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In: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850. ; 369, s. 8537-8558
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Journal article (peer-reviewed)abstract
- © 2017 American Mathematical Society. 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.
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