On moduli of pointed real curves of genus zero

Abstract

We introduce the moduli space $R{\bar{M}}_{2k,l}$ of pointed real curves of genus zero and give its natural stratification. The strata of $R{\bar{M}}_{2k,l}$ correspond to real curves of genus zero with different degeneration types and are encoded by their dual trees with certain decorations. By using this stratification, we calculate the first Stiefel-Whitney class of $R{\bar{M}}_{2k,l}$ and construct the orientation double cover $R{\tilde{M}}_{2k,l}$$of$R \bar{M}_{2k,l}$.

38 pages, 7 figures, minor grammar mistakes has been corrected

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