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On the Genus of Algebraic Curves [PDF]
Kyoto Journal of Mathematics, 1952 Yoshikazu Nakai
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Uniform algebras on curves [PDF]
Bulletin of the American Mathematical Society, 1969 H. Alexander
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On the algebra of elliptic curves [PDF]
Proceedings of the Edinburgh Mathematical Society, 2023 AbstractIt is argued that a nonsingular elliptic curve admits a natural or fundamental abelian heap structure uniquely determined by the curve itself. It is shown that the set of complex analytic or rational functions from a nonsingular elliptic curve to itself is a truss arising from endomorphisms of this heap.
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Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials
Comptes Rendus. Mathématique, 2023 The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura ...
Deroin, Bertrand, Matheus, Carlos
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Algebraic subgroups of the group of birational transformations of ruled surfaces [PDF]
Épijournal de Géométrie Algébrique, 2023 We classify the maximal algebraic subgroups of Bir(CxPP^1), when C is a smooth projective curve of positive genus.
Pascal Fong
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Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve
Journal of Mathematical Sciences and Modelling, 2021 In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr.
Moussa Fall
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The Hall algebra of a curve [PDF]
Selecta Mathematica, 2016 Let X be a smooth projective curve over a finite field. We describe H, the full Hall algebra of vector bundles X as a Feigin-Odesskii shuffle algebra. This shuffle algebra corresponds to the scheme S of all cusp eigenforms and to the rational function of two variables on S coming from the Rankin-Selberg L-functions.
Kapranov, M. +2 more
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On pseudopoints of algebraic curves [PDF]
Archiv der Mathematik, 2010 Following Kraitchik and Lehmer, we say that a positive integer $n\equiv1\pmod 8$ is an $x$-pseudosquare if it is a quadratic residue for each odd prime $p\le x$, yet is not a square. We extend this defintion to algebraic curves and say that $n$ is an $x$-pseudopoint of a curve $f(u,v) = 0$ (where $f \in \Z[U,V]$) if for all sufficiently large primes $p
Reza Rezaeian Farashahi +1 more
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An algebraic analysis of conchoids to algebraic curves [PDF]
Applicable Algebra in Engineering, Communication and Computing, 2008 8 ...
Sendra Pons, J. Rafael +1 more
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