Intersection Betti Numbers of the GIT Quotient of Quartic Plane Curves

The aim of this work is to present explicit computations for the intersection Betti numbers of the GIT quotient of the space of quartic plane curves and for the Betti numbers of a partial desingularization of this quotient, with respect to the action by change of coordinates of the special linear group. To achieve this, we calculate the equivariant cohomology over the so called HKKN stratification and employ Kirwan blow-ups as a fundamental technique.