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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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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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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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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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On the properties of hyperelliptic functions and isometries for Fuchsian groups isomorphism in \({\mathbb {D}}^2\) and \({\mathbb {H}}^2\)
This paper presents the conditions under which a coded digital communication system’s performance may be improved using better signal sets design...
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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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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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On Calculation of the Group of Automorphisms of Hyperelliptic Curves
We suggest an algorithm for finding the group of birational automorphisms of a hyperelliptic curve y 2 = p(x), p ∈ ℚ[x], over the field of complex...
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A Database of Group Actions on Riemann Surfaces
The automorphism group of a Riemann surface is an important object in a number of different mathematical fields. An algorithm of Thomas Breuer...
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On the 3-generated commutative rings of differential operators
The theory of commutative rings of differential operators relating the completely integrable systems with the geometry of algebraic curves was...
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COHOMOLOGICAL INVARIANTS OF THE STACK OF HYPERELLIPTIC CURVES OF ODD GENUS
We compute the cohomological invariants of ℋ g , the moduli stack of smooth hyperelliptic curves, for every odd g .
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Algebraic Function Fields of One Variable
Sections 4.1–4.4 survey the theory of functions of one variable; the Riemann–Roch Theorem; properties of holomorphy rings of function fields; and...
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On the problem of differentiation of hyperelliptic functions
We describe a construction that leads to an explicit solution of the problem of differentiation of hyperelliptic functions. A classical genus
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Siegel Modular Forms of Degree Two and Three and Invariant Theory
This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Cléry and Carel...
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Infinitesimal Variation Functions for Families of Smooth Varieties
In this paper we introduce some variation functions associated to the rank of the Infinitesimal Variations of Hodge Structure for a family of smooth...
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The P12-Theorem: The Classification of Surfaces and Its Historical Development
The Castelnuovo-Enriques classification of algebraic surfaces is based on the new ideas introduced by Federigo Enriques at the turn of the nineteenth...