Trigonal modular curves
نویسندگان
چکیده
منابع مشابه
Dihedral Coverings of Trigonal Curves
We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve D with a singular point of multiplicity (deg D−3).
متن کاملAbsolutely Simple Prymians of Trigonal Curves
As usual, Z,Q,C denote the ring of integers, the field of rational numbers and the field of complex numbers respectively. Let us fix a primitive cube root of unity ζ3 = −1+ √ −3 2 ∈ C. Let Q(ζ3) = Q( √ −3) be the third cyclotomic field and Z[ζ3] = Z +Z · ζ3 its ring of integers. We write λ for the (principal) maximal ideal (1− ζ3) · Z[ζ3] of Z[ζ3]. It is known [11, Th. 5 on p. 176] (see also [5...
متن کاملEffective radical parametrization of trigonal curves
Abstract. Let C be a non-hyperelliptic algebraic curve. It is known that its canonical image is the intersection of the quadrics that contain it, except when C is trigonal (that is, it has a linear system of degree 3 and dimension 1) or isomorphic to a plane quintic (genus 6). In this context, we present a method to decide whether a given algebraic curve is trigonal, and in the affirmative case...
متن کاملAbelian Functions for Trigonal Curves of Degree Four and Determinantal Formulae in Purely Trigonal Case
In the theory of elliptic functions, there are two kinds of determinantal formulae of Frobenius-Stickelberger [6] and of Kiepert [7], both of which connect the function σ(u) with ℘(u) and its (higher) derivatives through an determinantal expression. These formulae were naturally generalized to hyperelliptic functions by the papers [11], [12], and [13]. Avoiding generality, we restrict the story...
متن کاملModular Curves
H is the upper half plane, a complex manifold. It will be helpful to interpret H in multiple ways. A lattice Λ ⊂ C is a free abelian group of rank 2, for which the map Λ ⊗Z R → C is an isomorphism. In other words, Λ is a subgroup of C of the form Zα⊕Zβ, where {α, β} is basis for C/R. Two lattices Λ and Λ′ are homothetic if Λ′ = θΛ for some θ ∈ C∗. This is an equivalence relation, and the equiva...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1999
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-88-2-129-140