Small modifications of Mori dream spaces arising from ${\mathbb{C}}^{\ast }$-actions

Gianluca Occhetta, Eleonora A. Romano, Luis E. Solá Conde +1

We link small modifications of projective varieties with a ${\mathbb{C}}^{\ast }$-action to their GIT quotients. Namely, using flips with centers in closures of Białynicki-Birula cells, w…