We prove that, for any $g\ge 2$, the étale double cover ${\rho }_g:{\mathcal{E}}_g\to {\hat{\mathcal{E}}}_g$ from the moduli space ${\mathcal{E}}_g$ of complex polarized genus g Enriques surfaces to the moduli space ${\hat{\mathcal{E}}}_g$ of numerically polarized genus g Enriques surfaces is disconnected precisely over irreducible components of ${\hat{\mathcal{E}}}_g$ parametrizing 2-divisible classes, answering a question of Gritsenko and Hulek [13]. We characterize all irreducible components of ${\mathcal{E}}_g$ in terms of a new invariant of line bundles on Enriques surfaces that generalizes the ϕ-invariant introduced by Cossec [8]. In particular, we get a one-to-one correspondence between the irreducible components of ${\mathcal{E}}_g$ and 11-tuples of integers satisfying particular conditions. This makes it possible, in principle, to list all irreducible components of ${\mathcal{E}}_g$ for each $g\ge 2$.

我们证明，对于任何 $G\ge 2$，étale双层封面 ${\rho }_G：{\mathcal{Ë}}_G\to {\widehat{\mathcal{Ë}}}_G$ 从模空间 ${\mathcal{Ë}}_G$极化极化g Enriques曲面对模空间的分布${\widehat{\mathcal{Ë}}}_G$的数值偏振属克Enriques表面被断开的精确过束缚部件${\widehat{\mathcal{Ë}}}_G$参数化2可除的类，回答了Gritsenko和Hulek的问题[13]。我们表征了所有不可约成分${\mathcal{Ë}}_G$在上Enriques线束的新不变的术语表面，其概括了φ -invariant通过Cossec [8]引入。特别是，我们得到的不可约成分之间的一一对应关系${\mathcal{Ë}}_G$和满足特定条件的11元整数。原则上，这使得列出所有不可约成分成为可能。${\mathcal{Ë}}_G$ 每个 $G\ge 2$。