Moduli spaces of (polarised) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to isomorphism, only finitely many different moduli spaces of polarised Enriques surfaces. Here, we investigate the possible arithmetic groups and show that there are exactly 87 such groups up to conjugacy. We also show that all moduli spaces are dominated by a moduli space of polarised Enriques surfaces of degree 1240. Ciliberto, Dedieu, Galati and Knutsen have also investigated moduli spaces of polarised Enriques surfaces in detail. We discuss how our enumeration relates to theirs. We further compute the Tits building of the groups in question. Our computation is based on groups and indefinite quadratic forms and the algorithms used are explained.

中文翻译：

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偏振恩里克斯曲面的模量 - 计算方面

（极化）Enriques 曲面的模空间可以描述为正交类型模变体的开子集。Gritsenko 和 Hulek 表明，在同构之前，极化恩里克斯曲面仅存在有限多个不同的模空间。在这里，我们研究了可能的算术群，并表明总共有 87 个这样的群直至共轭。我们还表明，所有模空间都受 1240 度极化恩里克斯曲面的模空间支配。Ciliberto、Dedieu、Galati 和 Knutsen 也详细研究了极化恩里克斯曲面的模空间。我们讨论我们的列举与他们的列举有何关系。我们进一步计算相关组的 Tits 构建。我们的计算基于群和不定二次形式，并解释了所使用的算法。