On algebraic curves $$$$ of genus zero
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DOI: 10.1007/s00209-017-1889-9
Abstract: Using a geometric approach involving Riemann surface orbifolds, we provide lower bounds for the genus of an irreducible algebraic curve of the form $$\mathcal {E}_{A,B}:\, A(x)-B(y)=0$$ , where $$A, B\in \mathbb {C}(z)$$ . We also… read more here.
Keywords: genus zero; algebraic curves; curves genus;
A Geometric Investigation of the Invariant Algebraic Curves in Two Dimensional Lotka–Volterra Systems
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DOI: 10.1007/s11786-017-0311-7
Abstract: The aim of this work is to investigate the geometric behaviour of the invariant algebraic curves in two dimensional Lotka–Volterra systems, first classified by Moulin-Ollagnier. read more here.
Keywords: lotka volterra; two dimensional; curves two; algebraic curves ... See more keywords
Crossing the Transcendental Divide: From Translation Surfaces to Algebraic Curves
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DOI: 10.1080/10586458.2023.2203413
Abstract: We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified by translation. We use the theory… read more here.
Keywords: algebraic curves; transcendental divide; crossing transcendental; translation surfaces ... See more keywords
Values of Gaussian hypergeometric series and their connections to algebraic curves
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DOI: 10.1142/s179304211850001x
Abstract: In this paper, we explicitly evaluate certain special values of 2F1 hypergeometric series. These evaluations are based on some summation transformation formulas of Gaussian hypergeometric series. We find expressions of the number of points on… read more here.
Keywords: values gaussian; series connections; series; algebraic curves ... See more keywords
Geometry of webs of algebraic curves
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DOI: 10.1215/00127094-3715296
Abstract: A family of algebraic curves covering a projective variety $X$ is called a web of curves on $X$ if it has only finitely many members through a general point of $X$. A web of curves… read more here.
Keywords: differential geometry; geometry; algebraic curves; web structure ... See more keywords
Phase portraits of two classes of quadratic differential systems exhibiting as solutions two cubic algebraic curves
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DOI: 10.1515/dema-2022-0218
Abstract: Abstract The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R 2 {{\mathbb{R}}}^{2} , particularly for quadratic systems. Even with the… read more here.
Keywords: algebraic curves; differential systems; two classes; portraits two ... See more keywords