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Approximation in the Mean on Rational Curves
In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue...
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The Igusa Quartic and the Prym Map, with Some Rational Moduli
This paper is devoted to the ubiquity of the Igusa quartic $$ B \,\subset...
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The a-Number of Hyperelliptic Curves
It is known that for a smooth hyperelliptic curve to have a large a-number, the genus must be small relative to the characteristic of the field,...
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Flat Curves
We characterize the sextic trefoil among plane curves of low degree: first as a complex curve with compact, flat geometry; and then as a curve with...
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Theta characteristics of hyperelliptic graphs
We study theta characteristics of hyperelliptic metric graphs of genus g with no bridge edges. These graphs have a harmonic morphism of degree two to...
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On the Locus of Smooth Plane Curves with a Fixed Automorphism Group
Let M g be the moduli space of smooth, genus g curves over an algebraically closed field K of zero characteristic. Denote by M ...
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Witt’s Theorem for Noncommutative Conic Curves
Let k be a field. We extend the main result in Nyman (J. Algebra 434 , 90–114,
2015 ) to show that all homogeneous noncommutative curves of genus zero... -
A note on Gorenstein monomial curves
Let k be an arbitrary field. In this note, we show that if a sequence of relatively prime positive integers a = ( a 1 , a 2 , a 3 , a ...
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Gonality of non-Gorenstein curves of genus five
We establish sufficient conditions for some curves to be trigonal and derive from them that most of non-Gorenstein curves of genus five are so....
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The Korteweg-de Vries equation and a Diophantine problem related to Bernoulli polynomials
Some Diophantine equations related to the soliton solutions of the Korteweg-de Vries equation are resolved. The main tools are the connection with...
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Brill–Noether theory of curves on Enriques surfaces II: the Clifford index
We complete our study of linear series on curves lying on an Enriques surface by showing that, with the exception of smooth plane quintics, there are...
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A Canonical Curve of Genus 17
We compute equations for a Hurwitz curve of genus 17 and we conclude that the canonical ideal of any Hurwitz curve of genus 14 or 17 is generated by...
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On the Fundamental Groups of Non-generic \(\mathbb{R}\) -Join-Type Curves
An \(\mathbb{R}\)...
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The Trefoil
Dixon’s elliptic functions parameterize the real sextic trefoil curve by arc length and the complex curve as an embedded Platonic surface with 18 (or...