We study projective irreducible symplectic orbifolds of dimension four that are deformations of partial resolutions of quotients of hyperkähler manifolds of $K{3}^{[2]}$-type by symplectic involutions; we call them orbifolds of Nikulin type. We first classify those projective orbifolds that are really quotients, by describing all families of projective fourfolds of $K{3}^{[2]}$-type with a symplectic involution and the relation with their quotients, and then study their deformations. We compute the Riemann–Roch formula for Weil divisors on orbifolds of Nikulin type and using this we describe the first known locally complete family of singular irreducible symplectic varieties as double covers of special complete intersections $(3,4)$ in ${\mathbb{P}}^6$.

我们研究四维射影不可约辛轨道折叠，它是超卡勒流形的商的部分分辨率的变形$K{3}^{[2]}$- 辛对合类型；我们称它们为 Nikulin 类型的 Orbifolds。我们首先通过描述射影四重的所有族，对那些真正是商的射影轨道重进行分类$K{3}^{[2]}$- 具有辛对合的类型及其与商的关系，然后研究它们的变形。我们计算 Nikulin 型轨道折叠上 Weil 因子的黎曼-罗赫公式，并使用该公式将第一个已知的奇异不可约辛簇的局部完备族描述为特殊完全交集的双重覆盖$（3,4）$在${\mathbb{P}}^6$。