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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., Comment: 6 pages

We show that a quartic surface with an inner Galois point has the structure of an Eisenstein $K3$ surface of type $(4, 3)$. Furthermore we prove that the quartic surface with 8 (the maximum number) inner Galois points has not only this structure but also the structure of an Eisenstein $K3$ surface of type $(20, 1)$. In particular, it is isomorphic to Vinberg's $K3$ surface $X_{3}$, Comment: 10 pages

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., Comment: arXiv admin note: text overlap with arXiv:1808.03751

We show that there is only one log Enriques surface of index 7 and type $A_{15}$., Comment: 9 pages. arXiv admin note: text overlap with arXiv:1512.08647

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 And we describe fixed loci of non-symplectic automorphisms of order 21 and 42., Comment: This paper has been withdrawn by the author because it turns out that the main result is not true

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 N\'eron-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 N\'eron-Severi group, then we show that its rank is six., Comment: 15 pages

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., Comment: to appear in Trans. Amer. Math. Soc

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., Comment: 32 pages, to appear in Manuscripta Math

We treat non-symplectic automorphisms on $K3$ surfaces which act trivially on the N\'{e}ron-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., Comment: 15 pages

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., Comment: 28 pages; With an appendix by Shigeyuki Kondo. We add Smith exact sequences in the study of the fixed locus. To appear in Math. Z

In this paper, we study non-symplectic automorphisms of order 3 on algebraic $K3$ surface over $\mathbb{C}$ which act trivially on the N\'{e}ron-Severi lattice. In particular we shall characterize their fixed locus in terms of the invariants of 3-elementary lattices., Comment: 19 pages, to appear in Math. Nachr