18 citations · 44 across the 16 of their papers we have counts for
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Cubic Progressions on Smooth Plane Curves
Eslam Badr
Let $C \subset \Pbb^2_k$ be a smooth projective plane curve of degree over a number field . We prove that any cubic arithmetic or geometric progression sequence on …
On quadratic progression sequences on smooth plane curves
Eslam Badr, Mohammad Sadek
We study the arithmetic (geometric) progressions in the -coordinates of quadratic points on smooth projective planar curves defined over a number field . Unless the curve is…
Bielliptic smooth plane curves and quadratic points
Eslam Badr, Francesc Bars
Let be a smooth projective curve over a global field , which is neither rational nor elliptic. Harris-Silverman, when , and Schweizer, when together with an ext…
Hypersurface model-fields of definition for smooth hypersurfaces and their twists
Eslam Badr, Francesc Bars
Given a smooth projective variety of dimension defined over a perfect field that admits a non-singular hypersurface modelin over $\ove…
The Picard Group of Brauer-Severi Varieties
Eslam Badr, Francesc Bars, Elisa Lorenzo Garcia
In this note we provide explicit generators of the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular, for all Brauer-Severi surfaces. To pr…
Plane model-fields of definition, fields of definition, the field of moduli of smooth plane curves
Eslam Badr, Francesc Bars
Given a smooth plane curve of genus over an algebraically closed field , a field is said to be a \emph{plane model-f…