On blowing up the weighted projective plane

Juergen Hausen, Simon Keicher, Antonio Laface

Published 2016-08-16Version 1

We investigate the blow-up of a weighted projective plane at a general point. We provide criteria and algorithms for testing if the result is a Mori dream surface and we compute the Cox ring in several cases. Moreover applications to the study of $\overline{M}_{0,n}$ are discussed.