GIT Compactifications of from Conics

Abstract

We study geometric invariant theory (GIT) quotients parameterizing n-pointed conics that generalize the GIT quotients ⁠. Our main result is that admits a morphism to each such GIT quotient, generalizing the well-known result of Kapranov for the simpler quotients. Moreover, these morphisms factor through Hassett’s moduli spaces of weighted pointed rational curves, where the weight data comes from the GIT linearization data.