منابع مشابه
Gonality of modular curves in characteristic p
Let k be an algebraically closed field of characteristic p. Let X(p;N) be the curve parameterizing elliptic curves with full level N structure (where p N) and full level p Igusa structure. By modular curve, we mean a quotient of any X(p;N) by any subgroup of ((Z/peZ)× × SL2(Z/NZ)) /{±1}. We prove that in any sequence of distinct modular curves over k, the k-gonality tends to infinity. This exte...
متن کاملA linear lower bound on the gonality of modular curves
0.2. Remarks. The proof, which was included in the author’s thesis [א], follows closely a suggestion of N. Elkies. In the exposition here many details were added to the argument in [א]. We utilize the work [L-Y] of P. Li and S. T. Yau on conformal volumes, as well as the known bound on the leading nontrivial eigenvalue of the non-euclidean Laplacian λ1 ≥ 21 100 [L-R-S]. If Selberg’s eigenvalue ...
متن کاملGonality of a General Acm Curve in P
Let C be an ACM (projectively normal) nonsingular curve in PC not contained in a plane, and suppose C is general in its Hilbert scheme this is irreducible once the postulation is fixed. Answering a question posed by Peskine, we show the gonality of C is d − l, where d is the degree of the curve, and l is the maximum order of a multisecant line of C. Furthermore l = 4 except for two series of ca...
متن کاملOn the modular curve X0(23)
The Jacobian J0(23) of the modular curve X0(23) is a semi-stable abelian variety over Q with good reduction outside 23. It is simple. We prove that every simple semi-stable abelian variety over Q with good reduction outside 23 is isogenous over Q to J0(23). 2010 Mathematics Subject Classification. Primary 14L15; Secondary 11G18, 11R37.
متن کاملComputing the Degree of the Modular Parametrization of a Modular Elliptic Curve
The Weil-Taniyama conjecture states that every elliptic curve E/Q of conductor N can be parametrized by modular functions for the congruence subgroup T0(N) of the modular group r = F5L(2,Z). Equivalently, there is a nonconstant map ip from the modular curve Xq(N) to E . We present here a method of computing the degree of such a map for arbitrary N. Our method, which works for all subgroups ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.06.026