Seminar

Abstract: Enumerative geometry of curves in the complex projective plane is very classical. In this talk, we consider two generalisations of classical enumerative geometric problems of curves in the plane. We consider curves in  that lie inside a  in ; such curves are called planar curves. We discuss the enumeration of degree  planar curves in  having  nodes and another singularity of codimension , and that intersect  generic lines and pass through  generic points in , where  with . We also count the number of elliptic () curves of degree  in a del Pezzo surface  that pass through  generic points of .