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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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Explicit Formulas for Differentiation of Hyperelliptic Functions
AbstractThe paper provides an explicit solution to the well-known problem of differentiation of hyperelliptic functions with respect to parameters...
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Deformations of Hyperelliptic and Generalized Hyperelliptic Polarized Varieties
The purpose of this article is twofold. Firstly, we address and completely solve the following question: Let ( X , L ) be a smooth, hyperelliptic...
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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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Linear hyperelliptic Hodge integrals
We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for...
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General birationality and hyperelliptic theta divisors
We first state a condition ensuring that having a birational map onto the image is an open property for families of irreducible normal non uniruled...
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Weierstrass Semigroups from Cyclic Covers of Hyperelliptic Curves
The Weierstrass semigroup of pole orders of meromorphic functions in a point p of a smooth algebraic curve C is a classical object of study; a...
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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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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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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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Computing minimal Weierstrass equations of hyperelliptic curves
We describe an algorithm for determining a minimal Weierstrass equation for hyperelliptic curves over principal ideal domains. When the curve has a...
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Hyperelliptic odd coverings
We investigate a class of odd (ramification) coverings C → ℙ 1 where C is hyperelliptic, its Weierstrass points map to one fixed point of ℙ 1 and the...
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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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The Mumford Dynamical System and Hyperelliptic Kleinian Functions
AbstractWe develop a differential-algebraic theory of the Mumford dynamical system. In the framework of this theory, we introduce the
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