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Gorenstein curve singularities of genus three
We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of...
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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 Genus of an Algebraic Curve
Abel, lonely and unknown, was temporarily in Paris thanks to a travel grant from the government of Norway, and he hoped to win recognition in the...
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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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Orbifolds and the Modular Curve
We provide an account of the construction of the moduli stack of elliptic curves as an analytic orbifold. While intimately linked to Thurston’s point...
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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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A new characterisation of the Fermat curve
This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.
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Affine Cones over Fano–Mukai Fourfolds of Genus 10 are Flexible
We show that the affine cones over any Fano–Mukai fourfold of genus 10 are flexible in the sense of [1]. In particular, the automorphism group of...
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Liouvillian Solutions of Algebraic Ordinary Differential Equations of Order One of Genus Zero
This paper considers the class of autonomous algebraic ordinary differential equations (AODEs) of order one, and studies their Liouvillian general...
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Some results on the compactified Jacobian of a nodal curve
Let Y be an integral nodal curve. We show that the connected component of the moduli space of torsion free sheaves of rank 1 on the compactified...
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Splitting of the virtual class for genus one stable quasimaps
We analyze the local structure of the moduli space of genus one stable quasimaps. Combining it with the p-fields theory developed by Chang and Li...
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GOE statistics on the moduli space of surfaces of large genus
For a compact hyperbolic surface, we define a smooth linear statistic, mimicking the number of Laplace eigenvalues in a short energy window. We study...
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Classification of Exceptional Complements: Elliptic Curve Case
We classify the log del Pezzo surface (S, B) of rank 1 with no 1-,2-,3-,4-, or 6-complements with the additional condition that B has one irreducible...
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Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space
Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover...
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A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two
We prove a rigidity result for foliations on surfaces of genus two, which can be seen as a generalization to higher genus of Herman’s theorem on...