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Related papers: Automorphisms of K3 surfaces

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In this paper we present a classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven by describing the topological type of their fixed locus. In the case of purely non-symplectic automorphisms, we…

Algebraic Geometry · Mathematics 2022-12-06 Renee Bell , Paola Comparin , Jennifer Li , Alejandra Rincón-Hidalgo , Alessandra Sarti , Aline Zanardini

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…

Algebraic Geometry · Mathematics 2014-09-23 Dima Al Tabbaa , Alessandra Sarti , Shingo Taki

Nikulin and Vinberg proved that there are only a finite number of lattices of rank $\geq 3$ that are the N\'eron-Severi group of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric…

Algebraic Geometry · Mathematics 2022-02-17 Xavier Roulleau

We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperk\"ahler birational…

Algebraic Geometry · Mathematics 2022-09-27 Pietro Beri , Alberto Cattaneo

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…

Algebraic Geometry · Mathematics 2018-08-10 Shingo Taki

In this dissertation classification problems for K3-surfaces with finite group actions are considered. Special emphasis is put on K3-surfaces with antisymplectic involutions and compatible actions of symplectic transformations. Given a…

Algebraic Geometry · Mathematics 2009-02-24 Kristina Frantzen

We prove that a K3 surface with an automorphism acting on the global $2$-forms by a primitive $m$-th root of unity, $m \neq 1,2,3,4,6$, does not degenerate (assuming the existence of the so-called Kulikov models). A key result used to prove…

Algebraic Geometry · Mathematics 2023-12-27 Yuya Matsumoto

Let X be a complex algebraic K3 surface or a supersingular K3 surface in odd characteristic. We present an algorithm by which, under certain assumptions on X, we can calculate a finite set of generators of the image of the natural…

Algebraic Geometry · Mathematics 2015-02-10 Ichiro Shimada

We study automorphisms of order four on K3 surfaces. The symplectic ones have been first studied by Nikulin, they are known to fix six points and their action on the K3 lattice is unique. In this paper we give a classification of the purely…

Algebraic Geometry · Mathematics 2015-03-19 Michela Artebani , Alessandra Sarti

We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We…

Algebraic Geometry · Mathematics 2021-03-04 Paola Comparin , Nathan Priddis , Alessandra Sarti

The present paper provides several results on automorphisms of hyperk\"ahler (or irreducible holomorphic symplectic) manifolds. In particular it focuses on the symplectic case and contains a classification of prime order symplectic…

Algebraic Geometry · Mathematics 2013-03-20 Giovanni Mongardi

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

Smooth and symplectic symmetries of an infinite family of distinct exotic $K3$ surfaces are studied, and comparison with the corresponding symmetries of the standard $K3$ is made. The action on the $K3$ lattice induced by a smooth finite…

Geometric Topology · Mathematics 2008-09-11 Weimin Chen , Slawomir Kwasik

In this paper, we give a weak classification of locally linear pseudofree actions of the cyclic group of order 3 on a $K3$ surface, and prove the existence of such an action which can not be realized as a smooth action on the standard…

Geometric Topology · Mathematics 2007-06-13 Ximin Liu , Nobuhiro Nakamura

It is observed that the recent result of Voisin and earlier ones of the author suffice to prove in complete generality that symplectic automorphisms of finite order of a K3 surface X act as identity on the Chow group CH^2(X) of zero-cycles.

Algebraic Geometry · Mathematics 2013-09-12 Daniel Huybrechts

We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-K\"ahler metric. One motivation for this paper is the role of such…

Algebraic Geometry · Mathematics 2018-09-21 Frank Reidegeld

In this paper, we propose and study a conjecture that symplectic automorphisms of a $K3$ surface $X$ act trivially on the indecomposable part $\mathrm{CH}^2(X,1)_{\mathrm{ind}}\otimes \mathbb{Q}$ of Bloch's higher Chow group. This is a…

Algebraic Geometry · Mathematics 2025-09-18 Ken Sato

McMullen proved that there exists an automorphism of minimal topological entropy on a projective K3 surface. We derive equations for the surface and its automorphism. We reconstruct the surface and its automorphism from the Hodge theoretic…

Algebraic Geometry · Mathematics 2022-09-27 Simon Brandhorst , Noam D. Elkies

We classify finite groups acting by birational transformations of a non-trivial Severi--Brauer surface over a field of characteristc zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism…

Algebraic Geometry · Mathematics 2020-07-02 Constantin Shramov

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

Algebraic Geometry · Mathematics 2024-07-12 János Kollár