Projective models of Nikulin orbifolds

Abstract

We study projective fourfolds of $K{3}^{[2]}$-type with a symplectic involution and the deformations of their quotients, called orbifolds of Nikulin types; they are IHS orbifolds. We compute the Riemann--Roch formula for Weil divisors on such orbifolds and describe the first complete family of orbifolds of Nikulin type with a polarization of degree $2$ as double covers of special complete intersections $(3,4)$ in ${\mathbb{P}}^6$.

arXiv comment39 pages

References in corpus (8)

• Symplectic singularities
• The global moduli theory of symplectic varieties
• Induced Automorphisms on Irreducible Symplectic Manifolds
• Symplectic involutions of holomorphic symplectic fourfolds
• Symplectic involutions on deformations of K3^[2]
• Hyperkähler fourfolds and Kummer surfaces
• On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
• The double point formula with isolated singularities and canonical embeddings