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Faltings Heights of Hyperelliptic Curves over Function Fields
Faltings heights over function fields of complex projective curves are modular invariants of families of curves. The question on minimized Faltings...
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A hyperelliptic curve map** to specified elliptic curves
If an ordered 13-tuple ( E 1 , …, E 13 ) of elliptic curves over ℂ is sufficiently general, there is no hyperelliptic curve which admits a non-trivial...
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Computing torsion subgroups of Jacobians of hyperelliptic curves of genus 3
We introduce an algorithm to compute the structure of the rational torsion subgroup of the Jacobian of a hyperelliptic curve of genus 3 over the...
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Short homology bases for hyperelliptic hyperbolic surfaces
Given a hyperelliptic hyperbolic surface S of genus g ≥ 2, we find bounds on the lengths of homologically independent loops on S . As a consequence,...
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The Complex Multiplication Method for Genus 3 Curves
We consider the problem of constructing genus 3 curves defined over the complex field with the property that their Jacobians are simple and admit...
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The classification of rigid hyperelliptic fourfolds
We provide a fine classification of rigid hyperelliptic manifolds in dimension four up to biholomorphism and diffeomorphism. These manifolds are...
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Continued Fractions in Hyperelliptic Fields with an Arbitrarily Long Period
AbstractThe article proves the following statement: in any hyperelliptic field L defined over the field of algebraic numbers K which having...
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The modularity of elliptic curves over all but finitely many totally real fields of degree 5
We study the finiteness of low degree points on certain modular curves and their Atkin–Lehner quotients, and, as an application, prove the modularity...
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Uniformization of hyperelliptic curves as a systematic approach to establishing decision regions of hyperbolic signal sets
In this paper, we present a new approach to designing hyperbolic signal sets matched to groups using Whittaker’s proposal in the uniformization of...
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Tropical curves of hyperelliptic type
We introduce the notion of tropical curves of hyperelliptic type. These are tropical curves whose Jacobian is isomorphic to that of a hyperelliptic...
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Chapter 8 Monodromy of Hyperelliptic Abelian Integrals
Note that the theorem doesn’t say anything about the perturbation terms, it is purely topological. However, in generic cases of (i) we can conclude...
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Curves
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Tropical hyperelliptic curves in the plane
Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded...
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Elliptic Curves over the Rationals
This chapter covers prerequisites on elliptic curves over $$\mathbb...
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On smooth plane models for modular curves of Shimura type
In this paper we prove that there are finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater...
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Quadratic points on dynamical modular curves
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This...
