arXiv subjects
Publications and source records attributed to Shingo Taki.
We study quasi-Galois points, which are a generalization of Galois points. We characterize smooth quartic surfaces admitting a quasi-Galois point in terms of K3 surfaces with a certain involution, and provide a criterion for quasi-Galois points for quartic surfaces. Moreover, we also determine all quasi-Galois points of the Fermat quartic surface and show that it has exactly 28 quasi-Galois points.
This paper introduces a generalization of classical Galois points by extending the ambient space from standard projective spaces to weighted projective spaces. Specifically, the study focuses on smooth weighted hypersurfaces of degree 6 in $\mathbb{P}(1,1,1,3)$ (which are $K3$ surfaces) to determine the defining equations and the number of weighted Galois points. Furthermore, it characterizes these $K3$ surfaces with weighted Galois points in terms of their automorphisms.
We prove that there exists a one-to-one correspondence between smooth quartic surfaces with an outer Galois point and K3 surfaces with a certain automorphism of order 4. Furthermore, we characterize quartic surfaces with two or more outer Galois points as K3 surfaces.
We prove that there exists a one to one correspondence between smooth quartic surfaces with an inner Galois point and Eisenstein $K3$ surfaces of type $(4, 3)$. Furthermore we characterize the quartic surface with 8 (the maximum number) inner Galois points as a singular $K3$ surface.
This paper is a survey about $K3$ surfaces with an automorphism and log rational surfaces, in particular, log del Pezzo surfaces and log Enriques surfaces. It is also a reproduction on my talk at "Mathematical structures of integrable systems and their applications" held at Research Institute for Mathematical Sciences in September 2018.
We show that there is only one log Enriques surface of index 7 and type $A_{15}$.
In this note, we treat a pair of a K3 surface and a non-symplectic automorphism of order 7m (m=1, 3 and 6) on it. We show that if the fixed locus of a non-symplectic automorphism order 7 is "special" then the pair is unique up to isomorphism. And we describe fixed loci of non-symplectic automorphisms of order 21 and 42.
We classify K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the Néron-Severi group has rank 6, there are two possibilities and if its rank is 14, there are five possibilities. In particular if the action of the automorphism is trivial on the Néron-Severi group, then we show that its rank is six.
K3 surfaces with non-symplectic symmetry of order 3 are classified by open sets of twenty-four complex ball quotients associated to Eisenstein lattices. We show that twenty-two of those moduli spaces are rational.
We use classification of non-symplectic automorphisms of K3 surfaces to obtain a partial classification of log del Pezzo surfaces of index three. We can classify those with "Multiple Smooth Divisor Property", whose definition we will give. Our methods include the definition of right resolutions of quotient singularities of index three and some analysis of automorphism-stable elliptic fibrations on K3 surfaces. In particular we find several log del Pezzo surfaces of Picard number one with non-toric singularities of index three.
We treat non-symplectic automorphisms on $K3$ surfaces which act trivially on the Néron-Severi lattice. In this paper, we classify non-symplectic automorphisms of prime-power order, especially 2-power order on $K3$ surfaces, i.e., we describe their fixed locus.
In this paper, we study non-symplectic automorphisms of order 3 on algebraic $K3$ surface over $\mathbb{C}$ which act trivially on the Néron-Severi lattice. In particular we shall characterize their fixed locus in terms of the invariants of 3-elementary lattices.
In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new results for automorphisms of order 5 and 7 and alternative proofs for higher orders. Moreover, for any prime p, we identify the irreducible components of the moduli space of K3 surfaces with a non-symplectic automorphism of order p.