This work is a PhD thesis. First we provide some general context on wonderful varieties and moduli spaces of rational curves. Working over complex numbers we prove that the moduli space of rational curves with no marked points on the wonderful compactification of a symmetric space is not irreducible in general. Lastly we show that in the case of wonderful group compactifications the set of rational curves with no marked points and irreducible source is irreducible.
The Kodaira dimension of moduli spaces of curves with marked points, II
On the Kodaira dimension of the moduli space of hyperelliptic curves with marked points
Relations among divisors on the moduli space of curves with marked points
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