1,720,969 research outputs found
Geometric Lang-Vojta conjecture in P^2
Full text linkLang-Vojta conjecture is one of the most celebrated conjec- tures in Diophantine Geometry. Stated independently by Paul Vojta and Serge Lang the conjecture pre- dicts degeneracy of S-integral points in algebraic varieties of log-general type for a finite set of places S of a number field κ containing the infinite ones, provided that the divisor “at infinity” is a normal crossing divisor. This deep conjecture and his analogous formulations are among the main open problems in Number Theory, Complex Analysis and Arithmetic Algebraic Geometry.
This thesis contains the work of the author during his Ph.D. studies at the University of Udine under the supervision of Prof. Pietro Corvaja (and, partially, during his visit to Brown University under the supervision of Prof. Dan Abramovich), and it is centered around the function field version of Lang- Vojta conjecture for complements of curves in P2, with at most normal crossing singularities. The main part contains the proof of two cases of this conjecture, namely the non-split case for complements of degree four and three components divisors and the split case for very generic divisors of degree four with simple normal crossin
Greatest common divisor results on semiabelian varieties and a conjecture of Silverman
Full text linkHyperbolicity and Uniformity of Varieties of Log General type
No full textProjective varieties with ample cotangent bundle satisfy many notions of hyperbolicity, and one goal of this paper is to discuss generalizations to quasi-projective varieties. A major hurdle is that the naive generalization is false—the log cotangent bundle is never ample. Instead, we define a notion called almost ample that roughly asks that it is as positive as possible. We show that all subvarieties of a quasi-projective variety with almost ample log cotangent bundle are of log general type. In addition, if one assumes globally generated then we obtain that such varieties contain finitely many integral points. In another direction, we show that the Lang–Vojta conjecture implies the number of stably integral points on curves of log general type, and surfaces of log general type with almost ample log cotangent sheaf are uniformly bounded
INVITATION TO INTEGRAL AND RATIONAL POINTS ON CURVES AND SURFACES
No full textWe 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
Fibered threefolds and Lang-Vojta's conjecture over function fields
Full text linkUsing 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
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Uniformity of integral points in curves and surfaces
No full textNon UBCUnreviewedAuthor affiliation: University of WashingtonPostdoctora
- …
