Related papers: Finite Symplectic Actions on the K3 Lattice

We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the…

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…

We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain K\"ahler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated,…

We construct a K3 surface over an algebraically closed field of characteristic 2 which contains two sets of 21 disjoint smooth rational curves such that each curve from one set intersects exactly 5 curves from the other set. This…

In this paper, we study $Z_2$ actions on a cell complex X having the cohomology ring isomorphic to that of the wedge sum $P^2 (n) V S^{3n}$ or $S^n V S^{2n} V S^{3n}$. We determine the possible fixed point sets depending on whether or not X…

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well.…

We prove that, for p an odd prime, every finite p-group of rank 3 acts freely on a finite complex X homotopy equivalent to a product of three spheres.

This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…

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…

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…

We show that there exists an automorphism of a projective K3 surface with Picard number $2$ such that the trace of its action on the Picard lattice is $3$. Together with a result of K. Hashimoto, J. Keum and K. Lee, we determine the set of…

Given a symplectic manifold $(M,\omega)$ endowed with a proper Hamiltonian action of a Lie group $G$, we consider the action induced by a Lie subgroup $H$ of $G$. We propose a construction for two compatible Witt-Artin decompositions of the…

We show that if a 1-ended group $G$ acts geometrically on a CAT(0) space $X$ and $\bd X$ is separated by $m$ points then either $G$ is virtually a surface group or $G$ splits over a 2-ended group. In the course of the proof we study nesting…

We construct smooth actions of arbitrary compact Lie groups on complex projective spaces, such that the corresponding transformations arising from the group action do not preserve any symplectic structure on the complex projective space.

A hypergeometric group is a matrix group modeled on the monodromy group of a generalized hypergeometric differential equation. This article presents a fruitful interaction between the theory of hypergeometric groups and dynamics on K3…

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…

We give a complete characterization of Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. We deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold…

In this paper we investigate when the generic member of a family of K3 surfaces admitting a non--symplectic automorphism of finite order admits also a symplectic automorphism of the same order. We give a complete answer to this question if…

In any characteristic different from 2 and 5, Kond\=o gave an example of a K3 surface with a purely non-symplectic automorphism of order 50. The surface was explicitly given as a double plane branched along a smooth sextic curve. In this…