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Related papers: K3-surfaces with special symmetry

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This article primarily aims at classifying, on certain K3 surfaces, the elliptic fibrations induced by conic bundles on smooth del Pezzo surfaces. The key geometric tool employed is the Alexeev-Nikulin correspondence between del Pezzo…

Algebraic Geometry · Mathematics 2024-03-28 Paola Comparin , Pedro Montero , Yulieth Prieto-Montañez , Sergio Troncoso

We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves $C_1\times C_2$ by the diagonal action of either the group $\Z/p\Z$ or the group $\Z/2p\Z$. These K3 surfaces admit a non-symplectic…

Algebraic Geometry · Mathematics 2013-03-08 Alice Garbagnati , Matteo Penegini

We survey our contributions on the classification of elliptic fibrations on K3 surfaces with a non-symplectic involution. We place them in the more general framework of K3 surfaces with an involution without any hypothesis on its fixed…

Algebraic Geometry · Mathematics 2023-04-05 Alice Garbagnati , Cecília Salgado

In this paper we complete the classification of the elliptic fibrations on K3 surfaces which admit a non-symplectic involution acting trivially on the N\'eron--Severi group. We use the geometric method introduced by Oguiso and moreover we…

Algebraic Geometry · Mathematics 2018-06-11 Alice Garbagnati , Cecília Salgado

Over an algebraically closed field, various finiteness results are known regarding the automorphism group of a K3 surface and the action of the automorphisms on the Picard lattice. We formulate and prove versions of these results over…

Algebraic Geometry · Mathematics 2019-05-14 Martin Bright , Adam Logan , Ronald van Luijk

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

The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces and for generalized Kummer varieties. Here we extend our…

Algebraic Geometry · Mathematics 2025-02-24 Ljudmila Kamenova , Giovanni Mongardi , Alexei Oblomkov

In this paper we provide a complete classification of non-symplectic automorphisms of order nine of complex K3 surfaces.

Algebraic Geometry · Mathematics 2019-04-04 Michela Artebani , Paola Comparin , María Elisa Valdés

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and…

Algebraic Geometry · Mathematics 2019-02-15 Chiara Camere , Alberto Cattaneo , Andrea Cattaneo

In this note we interpret a recent result of Gaberdiel, Hohenegger and Volpato in terms of derived equivalences of K3 surfaces. We prove that there is a natural bijection between subgroups of the Conway group Co_1 with invariant lattice of…

Algebraic Geometry · Mathematics 2014-09-10 Daniel Huybrechts

Similarly to our papers I and II on the subject (see arXiv:1403.6061 and arXiv:1504.00326), we classify degenerations of codimension 2 and higher of Kahlerian K3 surfaces with finite symplectic automorphism groups. In parts I and II, it was…

Algebraic Geometry · Mathematics 2018-12-21 Viacheslav V. Nikulin

For each field $k$ of characteristic zero, we classify which groups act by automorphisms on a quartic del Pezzo surface over $k$. We also determine which groups act on $k$-rational, stably $k$-rational, or $k$-unirational quartic del Pezzo…

Algebraic Geometry · Mathematics 2023-08-16 Jonathan M. Smith

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 present finite sets of generators of the full automorphism groups of three singular K3 surfaces, on which the alternating group of degree 6 acts symplectically. We also present a finite set of generators of the full automorphism group of…

Algebraic Geometry · Mathematics 2015-10-13 Ichiro Shimada

Using results of our papers [19], [20] and [21] about classification of degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, we classify Picard lattices of Kahlerian K3 surfaces. By classification we understand…

Algebraic Geometry · Mathematics 2018-12-24 Viacheslav V. Nikulin

We prove the main Conjecture 4 of our paper arXiv:1403.6061v5, which leads to classification of degenerations of codimension one of Kahlerian K3 surfaces with finite symplectic automorphism groups.

Algebraic Geometry · Mathematics 2016-07-01 Viacheslav V. Nikulin

We exhibit an example of a K3 surface of Picard rank $14$ with a non-symplectic automorphism of order $16$ which fixes a rational curve and $10$ isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and…

Algebraic Geometry · Mathematics 2016-05-17 Jimmy Dillies

We analyze K3 surfaces admitting an elliptic fibration $E$ and a finite group $G$ of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration $E/G$ comparing its properties to the ones of…

Algebraic Geometry · Mathematics 2009-04-10 Alice Garbagnati

We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certain conjugacy classes of finite subgroups of the orthogonal…

Algebraic Geometry · Mathematics 2023-03-27 Simon Brandhorst , Tommy Hofmann

Let X be a K3 surface with an involution g which has non-empty fixed locus X^g and acts non-trivially on a non-zero holomorphic 2-form. We shall construct all such pairs (X, g) in a canonical way, from some better known double coverings of…

Algebraic Geometry · Mathematics 2007-05-23 D. -Q. Zhang