We compute the cohomology rings of smooth real toric varieties and of real toric spaces, which are quotients of real moment-angle complexes by freely acting subgroups of the ambient 2-torus. The differential graded algebra (dga) we present is in fact an equivariant dga model, valid for arbitrary coefficients. We deduce from our description that smooth toric varieties are $\hbox{M}$-varieties.

中文翻译：

---

真实复曲面空间的上同调环和光滑真实复曲面变体

我们计算了光滑实复曲面变体和实复曲面空间的上同调环，它们是由环境 2-环面的自由作用子群得到的实矩角复数的商。我们提出的微分分级代数 (dga) 实际上是一个等变 dga 模型，适用于任意系数。我们从我们的描述中推断出光滑复曲面变体是$\hbox{M​​}$ -varieties。