Rational points in the moduli space of genus two

Autor: Beshaj, L., Hidalgo, R., Kruk, S., Malmendier, A., Quispe, S., Shaska, T.

Publikováno v: Contemp. Math., 703, 83-115, Amer. Math. Soc., Providence, RI, 2018

We build a database of genus 2 curves defined over $\mathbb Q$ which contains all curves with minimal absolute height $h \leq 5$, all curves with moduli height $\mathfrak h \leq 20$, and all curves with extra automorphisms in standard form $y^2=f(x^2

Externí odkaz: http://arxiv.org/abs/1902.08279

Theta functions of superelliptic curves

Autor: Beshaj, L., Elezi, A., Shaska, T.

Publikováno v: Advances on superelliptic curves and their applications, 47--69, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS, Amsterdam, 2015

In this short survey we give a description of the theta functions of algebraic curves, half-integer theta-nulls, and the fundamental theta functions. We describe how to determine such fundamental theta functions and describe the components of the mod

Externí odkaz: http://arxiv.org/abs/1503.00297

Heights on algebraic curves

Autor: Beshaj, L., Shaska, T.

Publikováno v: Advances on superelliptic curves and their applications, 137--175, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS, Amsterdam, 2015

In these lectures we cover basics of the theory of heights starting with the heights in the projective space, heights of polynomials, and heights of the algebraic curves. We define the minimal height of binary forms and moduli height for algebraic cu

Externí odkaz: http://arxiv.org/abs/1406.5659

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