Bielliptic modular curves X0⁎(N)

Autor: Francesc Bars, Josep González

Publikováno v: Journal of Algebra. 559:726-759

Let N ≥ 1 be a integer such that the modular curve X 0 ⁎ ( N ) has genus ≥2. We prove that X 0 ⁎ ( N ) is bielliptic exactly for 69 values of N. In particular, we obtain that X 0 ⁎ ( N ) is bielliptic over the base field for all these value

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::deb27e2410d8a2a070ab451190cc9c6c
https://doi.org/10.1016/j.jalgebra.2020.02.028

Plane model-fields of definition, fields of definition, and the field of moduli for smooth plane curves

Autor: Eslam Badr, Francesc Bars

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

Let C / k ‾ be a smooth plane curve defined over k ‾ , a fixed algebraic closure of a perfect field k. We call a subfield k ′ ⊆ k ‾ a plane model-field of definition for C if C descends to k ′ as a smooth plane curve over k ′ , that is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b25937b412538d153156200447c062de
https://doi.org/10.1016/j.jnt.2018.07.010

Bielliptic quotient modular curves with N square-free

Autor: Mohamed Kamel, Francesc Bars, Josep González

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Let N ≥ 1 be an square free integer and let W N be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X 0 ( N ) such that the modular curve X 0 ( N ) / W N has genus at least two. We determine all pairs ( N , W N ) such that X 0

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fab003b036b1a5cc6510a23aecb77dba
https://ddd.uab.cat/record/240665

Non-singular plane curves with an element of 'large' order in its automorphism group

Autor: Eslam Badr, Francesc Bars

Publikováno v: International Journal of Algebra and Computation. 26:399-433

Let [Formula: see text] be the moduli space of smooth, genus [Formula: see text] curves over an algebraically closed field [Formula: see text] of zero characteristic. Denote by [Formula: see text] the subset of [Formula: see text] of curves [Formula:

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::526e72129bbde244ab574e844e71a22a
https://doi.org/10.1142/s0218196716500168

On twists of smooth plane curves

Autor: Eslam Badr, Francesc Bars, Elisa Lorenzo García

Publikováno v: Mathematics of Computation
Mathematics of Computation, American Mathematical Society, In press, 〈10.1090/mcom/3317〉
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Mathematics of Computation, American Mathematical Society, 2018, 88 (315), pp.421-438. ⟨10.1090/mcom/3317⟩
Mathematics of Computation, 2018, 88 (315), pp.421-438. ⟨10.1090/mcom/3317⟩

International audience; Given a smooth curve defined over a field $k$ that admits a non-singular plane model over $\overline{k}$, a fixed separable closure of $k$, it does not necessarily have a non-singular plane model defined over the field $k$. We

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6288ff049966089971086bf0e2eecb83
https://ddd.uab.cat/record/240667