3 citations · 13 across the 33 of their papers we have counts for
38 papers
Galois points for a finite graph
Satoru Fukasawa, Tsuyoshi Miezaki
This paper introduces the notion of a Galois point for a finite graph, using the theory of linear systems of divisors for graphs discovered by Baker and Norine. We present a new ch…
Descendants of algebraic curves admitting two Galois points
Satoru Fukasawa
A connection between Galois points of an algebraic curve and those of a quotient curve is presented; in particular, the notion of a descendant of algebraic curves admitting two Gal…
Algebraic-geometric codes with many automorphisms arising from Galois points
Satoru Fukasawa
A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.
Quasi-Galois points, II: Arrangements
Satoru Fukasawa, Kei Miura, Takeshi Takahashi
In Part I, the present authors introduced the notion of a quasi-Galois point, for investigating the automorphism groups of plane curves. In this second part, the number of quasi-Ga…
A new characterisation of the Fermat curve
Satoru Fukasawa
This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.
Galois lines for the quotient curve of the Hermitian curve by an involution
Satoru Fukasawa
The arrangement of all Galois lines for the quotient curve of the Hermitian curve by an involution in the projective 3-space is described, in terms of the geometry over finite fiel…
Galois points and rational functions with small value sets
Satoru Fukasawa
This paper presents a connection between Galois points and rational functions over a finite field with small value sets. This paper proves that the defining polynomial of any plane…
A generalization of Esteves--Homma's example of tangentially degenerate curves
Satoru Fukasawa
This paper presents a method of a construction of tangentially degenerate curves with a birational Gauss map, focusing on the non-classicality of automorphisms. This method describ…
Examples of plane rational curves with two Galois points in positive characteristic, II
Satoru Fukasawa, Katsushi Waki
It is proved that there exist plane rational curves of degree twelve (resp. twenty-four) with two different outer Galois points such that the Galois group at one of two Galois poin…
Algebraic curves admitting inner and outer Galois points
Satoru Fukasawa
There are two purposes in this article. One is to present a criterion for the existence of a birational embedding into a projective plane with inner and outer Galois points for alg…
An elementary abelian -cover of the Hermitian curve with many automorphisms
Herivelto Borges, Satoru Fukasawa
The full automorphism group of a certain elementary abelian -cover of the Hermitian curve in characteristic is determined. It is remarkable that the order of Sylow -gro…
A theorem of Montanucci and Zini for generalized Artin-Mumford curves and its application to Galois points
Satoru Fukasawa
An elementary proof of a theorem of Montanucci and Zini on the automorphism group of generalized Aritn-Schreier-Mumford curves is presented, with the argument of Korchmaros and Mon…
Galois lines for the Artin-Schreier-Mumford curve
Satoru Fukasawa
The arrangement of all Galois lines for the Artin-Schreier-Mumford curve in the projective 3-space is described. It may be surprising that there exist infinitely many Galois lines…
Algebraic curves with collinear Galois points
Satoru Fukasawa
A criterion for the existence of a birational embedding into a projective plane with three collinear Galois points for algebraic curves is presented. The extendability of an automo…
Algebraic curves admitting non-collinear Galois points
Satoru Fukasawa
A criterion for the existence of a birational embedding into a projective plane with non-collinear Galois points for algebraic curves is presented. A new example of a plane curve w…
Algebraic curves admitting the same Galois closure for two projections
Satoru Fukasawa, Kazuki Higashine, Takeshi Takahashi
A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is presented. As an application, it i…
A birational embedding with two Galois points for quotient curves
Satoru Fukasawa, Kazuki Higashine
A criterion for the existence of a birational embedding with two Galois points for quotient curves is presented. We apply our criterion to several curves, for example, some cyclic…
Galois points for double-Frobenius nonclassical curves
Herivelto Borges, Satoru Fukasawa
We determine the distribution of Galois points for plane curves over a finite field of elements, which are Frobenius nonclassical for different powers of . This family is an…
Galois points for the Dickson-Guralnick-Zieve curve
Satoru Fukasawa
The Dickson-Guralnick-Zieve curve over a finite field has been studied recently by Giulietti, Korchmaros and Timpanella in several points of view. In this short note, the distribut…
Galois lines for the Giulietti--Korchmáros curve
Satoru Fukasawa, Kazuki Higashine
We describe the arrangement of all Galois lines for the Giulietti--Korchmáros curve in the projective -space. As an application, we determine the set of all Galois points for a…
Plane curves possessing two outer Galois points
Satoru Fukasawa, Pietro Speziali
We classify plane curves possessing two Galois points and such that the associated Galois groups and $G_{…
A birational embedding with two Galois points for certain Artin-Schreier curves
Satoru Fukasawa, Kazuki Higashine
We show that two curves of Artin-Schreier type have a birational embedding into a projective plane with two Galois points. As a consequence, all curves with large automorphism grou…
Birational embeddings of the Hermitian, Suzuki and Ree curves with two Galois points
Satoru Fukasawa
We show that there exists a plane curve of degree with two inner Galois points whose smooth model is the Hermitian curve of degree , where is a power of the charac…
Examples of plane rational curves with two Galois points in positive characteristic
Satoru Fukasawa, Katsushi Waki
We present four new examples of plane rational curves with two Galois points in positive characteristic, and determine the number of Galois points for three of them. Our results ar…