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Related papers: On automorphisms group of some K3 surfaces

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For every supersingular $K3$ surface $X$ in characteristic 2, there exists a homogeneous polynomial $G$ of degree 6 such that $X$ is birational to the purely inseparable double cover of a projective plane defined by $w^2=G$. We present an…

Algebraic Geometry · Mathematics 2007-05-23 Ichiro Shimada

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…

Algebraic Geometry · Mathematics 2012-03-27 Shingo Taki

In this paper we determine which automorphisms of general smooth quartic surfaces $S\subset \mathbb{P}^3$ of Picard rank $2$ are restrictions of Cremona transformations of $\mathbb{P}^3$.

Algebraic Geometry · Mathematics 2025-05-06 Carolina Araujo , Daniela Paiva , Sokratis Zikas

The article revisits birational and biregular automorphisms of the Hilbert scheme of points on a K3 surface from the perspective of derived categories. Under the assumption that the K3 surface is generic, the birational and biregular…

Algebraic Geometry · Mathematics 2026-05-26 Ziqi Liu

Let X be a complex projective K3 surface, and let T(X) be its transcendental lattice; the characteristic polynomials of the isometries of T(X) induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic…

Algebraic Geometry · Mathematics 2024-05-02 Eva Bayer-Fluckiger

Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we…

Algebraic Geometry · Mathematics 2024-01-17 Zhuang He

We prove that the automorphism group of Hilbert square of a Cayley's K3 surface of Picard number 2 is the free product of three cyclic groups of order two. The generators are three Beauville involutions.

Algebraic Geometry · Mathematics 2024-03-13 Kwangwoo Lee

We give more details to our examples in [9] of K3 surfaces over C such that they have infinite automorphism group but it preserves some elliptic pencil of the K3

Algebraic Geometry · Mathematics 2020-06-09 Viacheslav V. Nikulin

A generic K3 surface of degree 2t is a general complex projective K3 surface whose Picard group is generated by the class of an ample divisor whose with respect to the intersection form is 2t. We show that if X is the Hilbert square of a…

Algebraic Geometry · Mathematics 2022-01-14 Simone Novario

We show the finiteness of the N\'eron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal…

Algebraic Geometry · Mathematics 2026-05-05 Koji Fujiwara , Keiji Oguiso , Xun Yu

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism…

Algebraic Geometry · Mathematics 2026-05-04 Hisanori Ohashi , Matthias Schütt

We determine the automorphism group of an open log K3 surface with irreducible boundary.

Algebraic Geometry · Mathematics 2024-07-12 János Kollár

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.…

Algebraic Geometry · Mathematics 2012-03-27 Hisanori Ohashi , Shingo Taki

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

Algebraic Geometry · Mathematics 2017-12-27 Igor Dolgachev

We construct a modular compactification via stable slc pairs for the moduli spaces of K3 surfaces with a nonsymplectic group of automorphisms under the assumption that some combination of the fixed loci of automorphisms defines an effective…

Algebraic Geometry · Mathematics 2026-02-24 Valery Alexeev , Philip Engel , Changho Han

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…

Algebraic Geometry · Mathematics 2010-12-27 Shingo Taki

We construct explicitly moduli curves of polarized supersingular K3 surfaces in characteristic 2 with Artin invariant 2. As an application, we detect a "jump" phenomenon in a family of automorphism groups of supersingular K3 surfaces with a…

Algebraic Geometry · Mathematics 2007-05-23 Ichiro Shimada

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…

Algebraic Geometry · Mathematics 2024-08-09 Kei Miura , Shingo Taki

The first part of this paper studied $\mathrm{GSp}_4$-type abelian varieties and the corresponding compatible systems of $\mathrm{GSp}_4$ representations. Techniques in \cite{BCGP} are applied to show that one can prove the potential…

Number Theory · Mathematics 2025-12-05 Chao Gu

We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1. We do this by proving that a distinguished connected component of the space of…

Algebraic Geometry · Mathematics 2017-02-22 Arend Bayer , Tom Bridgeland