Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties

Abstract

We define Enriques varieties as a higher dimensional generalization of Enriques surfaces and construct examples by using fixed point free automorphisms on generalized Kummer varieties. We also classify all automorphisms of generalized Kummer varieties that come from an automorphism of the underlying abelian surface. Higher dimensional Enriques varieties2.1. Irreducible holomorphic symplectic manifolds. A complex, compact, Kähler manifold X is called irreducible symplectic if X is simply connected and

Classification of automorphisms on a deformation family of hyper-Kähler four-folds by p -elementary lattices

“…Then: • It follows from [9, Proposition 5.17] that the fixed locus X G is never empty if p = 2. So one cannot produce new examples of Enriques varieties (see [8,33]) using finite quotients of IHS−K3 [2] other than quotients by (special) involutions. • If the group G acts on the K3 surface Σ, it induces a natural action on Σ [2] .…”

Smith theory and irreducible holomorphic symplectic manifolds

“…This result implies that it is not possible to construct Enriques varieties of dimension four and index three, as defined in Boissière-Nieper-Wißkirchen-Sarti [7] and Oguiso-Schroër [38], if one starts with deformations of Hilbert schemes of two points on a K3 surface. Let ξ be a primitive eleventh root of unity and consider the order 11 automorphism ϕ of C given by…”

Varieties with $\mathbb {P}$-units

“…Our notion of strict Enriques varieties is inspired by similar notions of higher dimensional analogues of Enriques surfaces due to Boissière, Nieper-Wißkirchen, and Sarti [BNWS11] and Oguiso and Schröer [OS11]. There are known examples of strict Enriques varieties of index 3 and 4.…”

“…In Section 3.4, we discuss a class of varieties which we call strict Enriques varieties. There are two different notions of Enriques varieties in the literature (see [BNWS11] and [OS11]) and our notion is the intersection of these two; see Proposition 3.14(iv). In Section 3.5, we quickly mention a generalisation; namely strict Enriques stacks.…”