Projective algebraic geometry
A projective algebraic variety is the locus of points of the projective space (over the complex field) satisfying a set of polynomial equations. In such a setup, the main object of study is the description of the properties of projective algebraic varieties which are invariant with respect to the natural action on the projective space of the linear group. A particular attention is focused on the study of configurations of points, curves, surfaces and secant varieties. Some algebro-geometric objects, called bundles, can be associated to such embedded algebraic varieties. The inspection of the properties of such bundles reflects on the projective geometry of the underlying varieties.