Monodromy of Projective Curves

الأصل · EN

The uniform position principle states that, given an irreducible nondegenerate curve C in the projective r-space Pʳ, a general (r-2)-plane L is uniform, that is, projection from L induces a rational map from C to P¹ whose monodromy group is the full symmetric group. In this paper we show the locus of non-uniform (r-2)-planes has codimension at least two in the Grassmannian for a curve C with arbitrary singularities. This result is optimal in P². For a smooth curve C in P³ that is not a rational curve of degree three, four or six, we show any irreducible surface of non-uniform lines is a Schubert cycle of lines through a point x, such that projection from x is not a birational map of C onto its image.