14 citations · 50 across the 18 of their papers we have counts for
19 papers
Exceptional loci in algebraic surfaces
Lucia Caporaso, Amos Turchet
We study the algebraic exceptional set for surfaces (S,B) of log general type, when B has at least three irreducible components; we prove that in most cases it is finite or empty.
On the role of secondary electrons in the color change of high-dose X-ray irradiated topaz
G. S. Elettivo, M. Ferraro, R. Filosa +4
Owing to its high brightness, synchrotron light allows for investigating with extreme precision the physical properties of matter. The irradiation with high-dose X-ray beams may al…
The algebraic Green-Griffiths-Lang conjecture for complements of very general pairs of divisors
Kenneth Ascher, Amos Turchet, Wern Yeong
We prove that the complement of a very general pair of hypersurfaces of total degree in is algebraically hyperbolic modulo a proper closed subvariety. This prov…
Tropical curves of unibranch points and hypertangency
Lucia Caporaso, Amos Turchet
We study integral plane curves meeting at a single unibranch point and show that such curves must satisfy two equivalent conditions. A numeric condition: the local invariants of th…
Hypertangency of plane curves and the algebraic exceptional set
Lucia Caporaso, Amos Turchet
We investigate plane curves intersecting in at most two unibranched points to study the algebraic exceptional set appearing in standard conjectures of diophantine and hyperbolic ge…
Rational distances from given rational points in the plane
Pietro Corvaja, Amos Turchet, Umberto Zannier
In this paper we study sets of points in the plane with rational distances from r prescribed points P_1, ...,P_r. A crucial case arises for r = 3, where we provide simple necessary…
Simply connectedness and hyperbolicity
Erwan Rousseau, Carlo Gasbarri, Amos Turchet +1
We generalize to arbitrary dimension our previous construction of simply connected weakly-special but not special varieties. We show that they satisfy the function field and comple…
Greatest Common Divisor results on semiabelian varieties and a Conjecture of Silverman
Fabrizio Barroero, Laura Capuano, Amos Turchet
A divisibility sequence is a sequence of integers such that divides if divides . Results of Bugeaud, Corvaja, Zannier, among others, have shown that th…
Some examples of exceptional loci in Vojta Conjecture
Amos Turchet
In this short note we discuss the exceptional locus for the Lang-Vojta's conjecture in the case of the complement of two completely reducible hyperplane sections in a cubic surface…
Divisibility of polynomials and degeneracy of integral points
Erwan Rousseau, Julie Tzu-Yueh Wang, Amos Turchet
We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties t…
Around the Chevalley-Weil Theorem
Pietro Corvaja, Amos Turchet, Umberto Zannier
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological t…
Hyperbolicity of varieties of log general type
Kenneth Ascher, Amos Turchet
These notes provide an overview of various notions of hyperbolicity for varieties of log general type from the viewpoint of both arithmetic and birational geometry. The main result…
Nonspecial varieties and Generalized Lang-Vojta conjectures
Erwan Rousseau, Amos Turchet, Julie Tzu-Yueh Wang
We construct a family of fibered threefolds such that has no étale cover that dominates a variety of general type but it dominates the orbifold of g…
Lang-Vojta Conjecture over function fields for surfaces dominating
Laura Capuano, Amos Turchet
We prove the nonsplit case of the Lang-Vojta conjecture over function fields for surfaces of log general type that are ramified covers of . This extends results of…
The Erdős-Ulam problem, Lang's conjecture, and uniformity
Kenneth Ascher, Lucas Braune, Amos Turchet
A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's Conjecture, that the cardinalities of…
Hyperbolicity and uniformity of varieties of log general type
Kenneth Ascher, Kristin DeVleming, Amos Turchet
Projective 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 ma…
A fibered power theorem for pairs of log general type
Kenneth Ascher, Amos Turchet
Let be a stably family with log canonical general fiber. We prove that, after a birational modification of the base , there is a morphism from a h…
Invitation to Integral and Rational points on curves and surfaces
Pranabesh Das, Amos Turchet
This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solution…
Fibered Threefolds and Lang-Vojta's Conjecture over Function Fields
Amos Turchet
Using the techniques introduced by Corvaja and Zannier we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a coni…