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Published in 2018 at "Mathematische Zeitschrift"
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…
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Keywords:
genus zero;
algebraic curves;
curves genus;
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Published in 2017 at "Mathematics in Computer Science"
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.
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Keywords:
lotka volterra;
two dimensional;
curves two;
algebraic curves ... See more keywords
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Published in 2022 at "Experimental Mathematics"
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…
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Keywords:
algebraic curves;
transcendental divide;
crossing transcendental;
translation surfaces ... See more keywords
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Published in 2018 at "International Journal of Number Theory"
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…
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Keywords:
values gaussian;
series connections;
series;
algebraic curves ... See more keywords
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1
Published in 2017 at "Duke Mathematical Journal"
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…
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Keywords:
differential geometry;
geometry;
algebraic curves;
web structure ... See more keywords
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Published in 2023 at "Demonstratio Mathematica"
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…
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Keywords:
algebraic curves;
differential systems;
two classes;
portraits two ... See more keywords