Mara Ungureanu: Intersections of secant varieties to algebraic curves

Title: Intersections of secant varieties to algebraic curves

Speaker: Mara Ungureanu

Abstract: For a smooth projective curve, the varieties parametrising its secant planes are among the most studied objects in classical enumerative geometry. In order to better understand their geometry, which in turn describes the extrinsic properties of the curve, one is lead to the study of Brill-Noether theory. This allows us to translate such extrinsic geometry problems in terms of objects belonging to the intrinsic geometry of the curve, namely subvarieties of its symmetric product. In this talk we shall introduce some basic notions of Brill-Noether theory, define secant varieties to a curve embedded in projective space and study some unexpected properties of their geometry that arise as non-transversality of intersections inside the symmetric product of the curve.

Keywords: enumerative geometry, algebraic curves, symmetric product, secant planes, Brill-Noether theory