Projective models of Nikulin orbifolds

TL;DR

This paper investigates projective fourfolds of K3^{[2]}-type with symplectic involutions, analyzing their orbifold quotients, computing Riemann--Roch formulas, and constructing a family of Nikulin-type orbifolds with degree 2 polarization.

Contribution

It introduces the first complete family of Nikulin-type orbifolds with degree 2 polarization as double covers of specific complete intersections.

Findings

Computed Riemann--Roch formula for Weil divisors on Nikulin orbifolds.

Described a family of Nikulin orbifolds with degree 2 polarization.

Constructed orbifolds as double covers of (3,4) complete intersections in projective space.

Abstract

We study projective fourfolds of $K3^{[2]}$-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 $\mathbb{P}^6$.