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Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2018, Volume 222, Issue 7, pp. 1810 - 1826
Let K be the algebraic closure of a finite field Fq of odd characteristic p. For a positive integer m prime to p, let F=K(x,y) be the transcendence degree 1... 
MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAIC-CURVES
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 4, pp. 2018 - 2034
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2018, Volume 370, Issue 1, pp. 131 - 196
From a topological viewpoint, a rational curve in the real projective plane is generically a smoothly immersed circle and a finite collection of isolated... 
TOPOLOGY | MATHEMATICS | ALGEBRAIC-CURVES | Mathematics - Algebraic Geometry
Journal Article
Journal of Number Theory, ISSN 0022-314X, 05/2018, Volume 186, pp. 259 - 268
Given a curve C over a field K, the period of C/K is the gcd of degrees of K-rational divisor classes, while the index is the gcd of degrees of K-rational... 
Period | Index | Algebraic curves | MATHEMATICS | FIELDS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2015, Volume 430, Issue 1, pp. 354 - 380
Journal Article
Journal of Algebra, ISSN 0021-8693, 05/2019, Volume 526, pp. 30 - 50
Let X be a (projective, non-singular, irreducible) curve of even genus g(X)≥2 defined over an algebraically closed field K of characteristic p. If the p-rank... 
Automorphism groups | p-Rank | Algebraic curves | MATHEMATICS | FUNCTION-FIELDS
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 06/2017, Volume 108, Issue 6, pp. 593 - 600
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 09/2019, Volume 357, pp. 302 - 318
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not... 
Similarity | Harmonic polynomials | Dihedral groups | Planar algebraic curves | Symmetry detection | MATHEMATICS, APPLIED | Analysis | Algorithms
Journal Article
2008, STU - Student edition, Princeton series in applied mathematics, ISBN 9780691096797, xx, 696
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental... 
Mathematics | Curves, Algebraic | Finite fields (Algebra)
Book
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2018, Volume 2018, Issue 32, pp. 1 - 18
In this paper we study the existence and uniqueness of limit cycles for socalled quadratic systems with a symmetrical solution: dx(t)/dt = P-2(x,y) equivalent... 
Ordinary differential equations | Algebraic curve | Limit cycle | EXISTENCE | MATHEMATICS | ordinary differential equations | MATHEMATICS, APPLIED | limit cycle | INVARIANT ALGEBRAIC-CURVES | algebraic curve | LIMIT-CYCLES | UNIQUENESS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 162 - 211
Let X be a (projective, geometrically irreducible, non-singular) algebraic curve of genus g≥2 defined over an algebraically closed field K of odd... 
Automorphism groups | Algebraic curves | Positive characteristic | FINITE SIMPLE-GROUPS | MATHEMATICS | NUMBER | SUBGROUPS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 09/2015, Volume 154, pp. 278 - 291
Let M be the Artin–Mumford curve over the finite prime field Fp with p>2. By a result of Valentini and Madan, AutFp(M)≅H with H=(Cp×Cp)⋊Dp−1. We prove that if... 
Automorphism groups | Finite fields | Algebraic curves | MATHEMATICS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2019, Volume 372, Issue 7, pp. 4805 - 4827
Given a real hyperelliptic algebraic curve X with non-empty real part and a real effective divisor \mathcal {D} arising via pullback from \mathbb{P}^1 under... 
MATHEMATICS | real linear series | real algebraic curves | tropical geometry | real inflection points | Real enumerative algebraic geometry
Journal Article
Journal of Algebra, ISSN 0021-8693, 09/2017, Volume 485, pp. 310 - 331
Let Fq be the finite field of order q=ph with p>2 prime and h>1, and let Fq¯ be a subfield of Fq. From any two q¯-linearized polynomials L1,L2∈F‾q[T] of degree... 
Finite fields | Automorphism groups | Algebraic curves | Algebraic function fields | MATHEMATICS
Journal Article
Journal of Algebra, ISSN 0021-8693, 12/2016, Volume 468, pp. 253 - 274
In this paper we investigate the space of R-places of an algebraic function field of one variable. We deal with the problem of determining when two orderings... 
Real algebraic curve | Space of cuts | Space of orderings | [formula omitted]-places | Algebraic function field | R-places | MATHEMATICS | ALGEBRAIC-CURVES | REAL
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 03/2011, Volume 52, Issue 3, pp. 032703 - 032703-13
We give a complete characterization of the Darbouxian first integrals of a generalized Raychaudhuri equation which appears in modern string cosmology and which... 
PHYSICS, MATHEMATICAL | INVARIANT ALGEBRAIC-CURVES
Journal Article
Journal of Algebra, ISSN 0021-8693, 11/2019, Volume 538, pp. 290 - 311
Two classical results in algebraic geometry are that the branch curve of a del Pezzo surface of degree 1 can be embedded as a space sextic curve in P3 and that... 
Theta characteristics | Algebraic curves | Del Pezzo surfaces | Tritangents | Space sextic | MATHEMATICS | Buildings | Remodeling, restoration, etc | Algorithms
Journal Article
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