Geometric compactification of moduli space of cubic surfaces and Kirwan blowup

[摘要] We compactify the moduli space of cubic surfaces by constructing a moduli stack of stable cubic and triploid surfaces, together with a projective coarse moduli space. We also give a detailed geometric interpretation. This compactification coincides with the Naruki Cross Ratio Variety. We also show that this compactification can be obtained by taking a certain weighted blowup along the strictly semi-stable stratum from Kirwan;;s stratification and partial desingularization procedures.

[发布机构] Rice University