arXiv subjects

Keika Shimahara

Publications and source records attributed to Keika Shimahara.

3 recordsLinked to original sources

arXiv2025

Large orders of automorphisms of smooth curves in $\mathbb P^1\times \mathbb P^1$

For $a,b\geq 3$, we calculate the orders of automorphisms of smooth curves with bidegree $(a,b)$ in the product $\pp$ of the projective line $\mathbb P^1$. We identify smooth curves in $\pp$ which have automorphisms with the largest orders. In addition, we study the relationship between symmetry and geometric structure of curves. We provide a sufficient condition for the quotient space by an automorphism to be $\mathbb P^1$.

math.AG↗

arXiv2025

Subgroups of the Projective Linear Group Realized by wild Galois Points

We work over an algebraically closed field of positive characteristic. This paper investigates linear representations of Galois groups arising from wild Galois points on projective hypersurfaces. We prove that these Galois groups lift to the general linear group and act naturally on vector spaces. Furthermore, we establish necessary and sufficient conditions for subgroups of the projective linear group to be realized as Galois groups of wild Galois points. In addition, we show that projections from wild Galois points on normal hypersurfaces are necessarily wildly ramified. We provide a geometric criterion for detecting wild ramification via the fixed loci of birational automorphisms, linking group-theoretic properties to the geometry of the hypersurface.

math.AG↗

arXiv2025

Persistence of Galois property of hypersurfaces over algebraic integers across other characteristics

In this paper, we investigate hypersurfaces defined over a ring of algebraic integers, and show that if the projection from a point induces a Galois extension over either a number field or the residue field associated with a prime ideal satisfying certain conditions, then the Galois property persists under reduction modulo the residue field associated with all but finitely many such prime ideals. Furthermore, for quartic hypersurfaces, we provide necessary and sufficient conditions for the Galois group to be given by a projective linear group, depending on the characteristic of the base field.

math.AG↗