On the variety of the inflection points of plane cubic curves

Abstract

In this paper we study properties of the nine-dimensional variety of the inflection points of plane cubics. We describe the local monodromy groups of the set of inflection points near singular cubic curves and give 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 cubics. We also prove the vanishing of the irregularity of a smooth manifold birationally isomorphic to the variety of the inflection points of plane cubics.