Related papers: Algebraic curves admitting the same Galois closure…
A criterion for the existence of a birational embedding of an algebraic curve into a projective plane with two Galois points is presented. Several novel examples of plane curves with two inner Galois points as an application are described.
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 algebraic curves. Another is to classify plane curves of degree…
For a plane curve, a point in the projective plane is said to be Galois when the point projection induces a Galois extension of function fields. We give a new characterization of a Fermat curve whose degree minus one is a power of $p$ in…
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 with non-collinear Galois points as an application is…
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 automorphism induced by a Galois point to a linear transformation…
We study the relationship between rational points and Galois points for a plane curve over a finite field. It is known that the set of Galois points coincides with that of rational points of the projective plane if the curve is the…
A criterion for the existence of a plane model with two non-smooth Galois points for algebraic curves is presented, which is a generalization of Fukasawa's criterion for two smooth Galois points. Owing to this generalized criterion,…
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 fields. All Galois points for three plane models of this curve…
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 are related to a problem on projective linear groups.
Let $\mathcal{C}$ be an irreducible plane curve of $\text{PG}(2,\mathbb{K})$ where $\mathbb{K}$ is an algebraically closed field of characteristic $p\geq 0$. A point $Q\in \mathcal{C}$ is an inner Galois point for $\mathcal{C}$ if the…
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 Galois points is introduced. It is shown that all descendants…
We show that there exists a plane curve of degree $q^3+1$ with two inner Galois points whose smooth model is the Hermitian curve of degree $q+1$, where $q$ is a power of the characteristic $p>0$. Similar results hold for the Suzuki and Ree…
A point on a plane curve is said to be Galois (for the curve) if the projection from the point as a map from the curve to a line induces a Galois extension of function fields. It is known that the number of Galois points is finite except…
We give new examples of plane curves with two or more Galois points as a family, and describe the number of Galois points for these curves, by using finite fields.
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 subcovers of the Giulietti-Korchmaros curve or of the curves…
We introduce the new notion of the "quasi-Galois point" in Algebraic geometry, which is a generalization of the Galois point. A point $P$ in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial…
We classify plane curves $\mathcal{C}$ possessing two Galois points $P_1$ and $P_2 \in \mathbb{P}^2 \setminus \mathcal{C}$ such that the associated Galois groups $G_{P_1}$ and $G_{P_2}$ generate the semidirect product $G_{P_1}\rtimes…
For a plane curve, a point on the projective plane is said to be Galois if the projection from the point as a map from the curve to a line induces a Galois extension of function fields. We present upper bounds for the number of Galois…
Let $C$ be a smooth plane curve. A point $P$ in the projective plane is said to be Galois with respect to $C$ if the function field extension induced from the point projection from $P$ is Galois. We denote by $\delta(C)$ (resp.…
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 points is an alternating group $A_4$ (resp. a symmetric group…