We prove that a certain Brill-Noether locus over a non-hyperelliptic curve C of genus 4, is isomorphic to the Donagi-Izadi cubic threefold in the case when the pencils of the two trigonal line bundles of C coincide.
On this paper we compute the numerical function of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.
Let be a curve of genus defined over the fraction field of a complete discrete valuation ring with algebraically closed residue field. Suppose that and that the characteristic of the residue field is not . Suppose that the Jacobian has semi-stable reduction over . Embed in using a -rational point. We show that the coordinates of the torsion points lying on lie in the unique tamely ramified quadratic extension of the field generated over by the coordinates of the -torsion...
In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
This article is a short version of the paper published in J. Number Theory 145 (2014) but we add new results and a brief discussion about the Torsion Conjecture. Consider the family of superelliptic curves (over ℚ) , and its Jacobians , where 2 < q < p are primes. We give the full (resp. partial) characterization of the torsion part of (resp. ). The main tools are computations of the zeta function of (resp. ) over for primes l ≡ 1,2,4,8,11 (mod 15) (resp. for primes l ≡ -1 (mod qp))...