Cubic hypersurfaces are important examples of algebraic varieties, and it is interesting to understand their geometric properties and numerical invariants. In this talk we will focus on complex cubic threefolds, that is, hypersurfaces of degree three in complex projective four-space. We will present a classification of isolated singularities appearing on cubic threefolds. Then we will use the classification to compute certain invariants of singular cubic threefolds, including the cohomology groups. Time permitting, we will explain the connection of our results to a construction of a Hyperkähler manifold of deformation type O’Grady 10 due to Laza, Saccà and Voisin. This talk is based on a joint work with Lisa Marquand.
