1,720,979 research outputs found
Betti maps, Pell equations in polynomials and almost-Belyi maps
Full text linkWe study the Betti map of a particular (but relevant) section of the family of Jacobians of hyperelliptic curves using the polynomial Pell equation A(2) - DB2 = 1, with A, B, D is an element of C[t] and certain ramified covers P-1 -> P-1 arising from such equation and having heavy constrains on their ramification. In particular, we obtain a special case of a result of Andre, Corvaja and Zannier on the submersivity of the Betti map by studying the locus of the polynomials D that fit in a Pell equation inside the space of polynomials of fixed even degree. Moreover, Riemann existence theorem associates to the abovementioned covers certain permutation representations: We are able to characterize the representations corresponding to 'primitive' solutions of the Pell equation or to powers of solutions of lower degree and give a combinatorial description of these representations when D has degree 4. In turn, this characterization gives back some precise information about the rational values of the Betti map
Unlikely intersections in families of abelian varieties and the polynomial Pell equation
Full text linkLet be a smooth irreducible curve defined over a number field and consider an abelian scheme over and a curve inside , both defined over . In previous works, we proved that, when is a fibered product of elliptic schemes, if is not contained in a proper subgroup scheme of , then it contains at most finitely many points that belong to a flat subgroup scheme of codimension at least 2. In this article, we continue our investigation and settle the crucial case of powers of simple abelian schemes of relative dimension . This, combined with the above mentioned result and work by Habegger and Pila, gives the statement for general abelian schemes which has applications in the study of solvability of almost-Pell equations in polynomials
Unlikely intersections of curves with algebraic subgroups in semiabelian varieties
Full text linkLet G be a semiabelian variety and C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over Q ̄. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case
Linear relations in families of powers of elliptic curves
Full text linkMotivated by recent work of Masser and Zannier on simultaneous torsion on the Legendre elliptic curve Eλof equation Y2= X (X − 1)(X − λ), we prove that, given n linearly independent points P1(λ),..., Pn(λ) on Eλwith coordinates in Q(λ), there are at most finitely many complex numbers λ0 such that the points P1(λ0),..., Pn(λ0) satisfy two independent relations on Eλ0. This is a special case of conjectures about unlikely intersections on families of abelian varieties
L'antico, gli antichi. Batoni e l'ambiente erudito romano
No full textIl saggio analizza il rapporto dell'artista con la cultura antiquaria del tempo, il cui indiscusso epicentro era la città di Roma
Unlikely intersections in products of families of elliptic curves and the multiplicative group
Full text linkLet Eλbe the Legendre elliptic curve of equation Y2= X (X - 1)(X - l). We recently proved that, given n linearly independent points P1(l), 1⁄4, Pn(l) on Eλwith coordinates in (l), there are at most finitely many complex numbers l0such that the points P1(l0), 1⁄4, Pn(l0) satisfy two independent relations on El0. In this article, we continue our investigations on Unlikely Intersections in families of abelian varieties, and consider the case of a curve in a product of two non-isogenous families of elliptic curves and in a family of split semi-abelian varieties
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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
- …
