Singular Curves of Low Degree and Multifiltrations from Osculating Spaces

In order to study projections of smooth curves and the singularities of the image curve, we introduce multifiltrations obtained by combining flags of osculating spaces. In our research we classify all configurations of singularities occurring for a projection of a smooth curve embedded by a complete linear system away from a projective linear space of dimension at most two. In particular, we determine all configurations of singularities of non-degenerate degree d rational curves in P^n when d-n <4 and d<2n. During the talk I will focus on an illustrative example. The set of linear spaces giving a fixed singularity type is related to a specific Schubert cycle (which depends on the singularity). Based on a joint work with Nathan Ilten and Emanuele Ventura, https://arxiv.org/abs/1905.11860, International Mathematical Research Notices.