The group studies projective varieties. In particular we study rational plane curves and their singularities, with an emphasis on the relations with the splitting of the tangent bundle on their normalization and on the study of the minimal resolutions of zero dimensional schemes.
Secant varieties to rational normal curves are also used to study singularities of plane rational curves using their parametrization.
Applications of multiplicity theory and intersection theory to classical algebraic geometry are also pursued (singularities, degrees of secant varieties, computations of apparent double points on surfaces, etc.), also with the aid of computer algebra.
Elliptic fibrations. Noether-Lefschetz problems and applications.