On the variety of the inflection points of plane cubic curves

Abstract

In the paper, we investigate properties of the nine-dimensional variety of the inflection points of the plane cubic curves. The description of local monodromy groups of the set of inflection points near singular cubic curves is given. Also, it is given a detailed description of the normalizations of the surfaces of the inflection points of plane cubic curves belonging to general two-dimensional linear systems of cubic curves, The vanishing of the irregularity a smooth manifold birationally isomorphic to the variety of the inflection points of the plane cubic curves is proved.