Related papers: Bloch's conjecture for (anti-)autoequivalences on …

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…

A holomorphic torsion invariant of K3 surfaces with involution was introduced by the second-named author. In this paper, we completely determine its structure as an automorphic function on the moduli space of such K3 surfaces. On every…

According to the Bloch-Beilinson conjectures, an automorphism of a K3 surface X that acts as the identity on the transcendental lattice should act trivially on CH^2(X). We discuss this conjecture for symplectic involutions and prove it in…

We provide new examples of anti-symplectic involutions on moduli spaces of stable sheaves on K3 surfaces. These involutions are constructed through (anti) autoequivalences of the bounded derived category of coherent sheaves on K3 surfaces…

Let $S$ be a smooth projective surface with $p_g=0$, let $\iota $ be a regular involution acting on $S$, and let $W$ be the resolution of singularities of the quotient surface $S/\iota $. In the paper we prove that Bloch's conjecture holds…

Symplectic involutions of a K3 surface are those involutions which leave the holomorphic 2-form invariant. We show, as predicted by Bloch's conjecture, that they act trivially on the CH_0 group of the K3 surface. This was recently proved by…

Bloch's conjecture for a surface $X$ over an algebraically closed field $k$ states that every homologically trivial correspondence $\Gamma $ acts as 0 on the Albanese kernel $T(X_{\Omega})$, where $\Omega $ is a universal domain containing…

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,…

This is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good…

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…

In this paper we study K3 surfaces with a non-symplectic automorphism of order 3. In particular, we classify the topological structure of the fixed locus of such automorphisms and we show that it determines the action on cohomology. This…

Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a…

This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to…

We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for $K3$ surfaces by constructing big line bundles of low degree on certain moduli…

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we…

This paper aims to establish the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties.…

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…

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…

Based on a novel application of an archimedean type pairing to the geometry and deformation theory of $K3$ surfaces, we construct a regulator indecomposable $K_1$-class on a self-product of a $K3$ surface. In the Appendix, we explain how…

We show that for any $N>0$ there exists a natural even $n>N$ such that the discriminant of moduli of K3 surfaces of the degree $n$ is not equal to the set of zeros of any automorphic form on the corresponding IV type domain. We give the…