Eslam Badr
Cairo University
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Featured researches published by Eslam Badr.
International Journal of Algebra and Computation | 2016
Eslam Badr; Francesc Bars
Let Mg be the moduli space of smooth, genus g curves over an algebraically closed field K of zero characteristic. Denote by Mg(G) the subset of Mg of curves δ such that G (as a finite nontrivial group) is isomorphic to a subgroup of Aut(δ) and let Mg(G) be the subset of curves δ such that G≅Aut(δ), where Aut(δ) is the full automorphism group of δ. Now, for an integer d ≥ 4, let MgPl be the subset of Mg representing smooth, genus g curves that admit a non-singular plane model of degree d (in this case, g = 1 2(d − 1)(d − 2)) and consider the sets MgPl(G) := M gPl ∩ M g(G) and MgPl(G) := M g(G) ∩ MgPl. In this paper we first determine, for an arbitrary but a fixed degree d, an algorithm to list the possible values m for which MgPl(ℤ/mℤ) is non-empty, where ℤ/mℤ denotes the cyclic group of order m. In particular, we prove that m should divide one of the integers: d − 1, d, d2 − 3d + 3, (d − 1)2, d(d − 2) or d(d − 1). Secondly, consider a curve δ ∈ MgPl with g = 1 2(d − 1)(d − 2) such that Aut(δ) has an el...
Mathematics of Computation | 2017
Eslam Badr; Francesc Bars; Elisa Lorenzo García
Given a smooth curve defined over a field
Archiv der Mathematik | 2018
Eslam Badr; Rubén A. Hidalgo; Saúl Quispe
k
Journal of the Egyptian Mathematical Society | 2014
Mohammed A. Saleem; Eslam Badr
that admits a non-singular plane model over
Mediterranean Journal of Mathematics | 2016
Eslam Badr; Francesc Bars
\overline{k}
arXiv: Algebraic Geometry | 2015
Eslam Badr; Francesc Bars
, a fixed separable closure of
Journal of Number Theory | 2019
Eslam Badr; Francesc Bars
k
arXiv: Number Theory | 2018
Eslam Badr; Francesc Bars
, it does not necessarily have a non-singular plane model defined over the field
arXiv: Number Theory | 2018
Eslam Badr; Francesc Bars
k
arXiv: Algebraic Geometry | 2018
Eslam Badr
. We determine under which conditions this happens and we show an example of such phenomenon. Now, even assuming that such a smooth plane model exists, we wonder about the existence of non-singular plane models over