Monodromy of Projective Curves

Gian Pietro Pirola; Enrico Schlesinger

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arXiv · math/0312375

Monodromy of Projective Curves

Gian Pietro Pirola·Enrico Schlesinger

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Abstract

The uniform position principle states that, given an irreducible nondegenerate curve C in the projective r-space $P^r$, a general (r-2)-plane L is uniform, that is, projection from L induces a rational map from C to $P^1$ 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 $P^2$. For a smooth curve C in $P^3$ 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.

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Gian Pietro Pirola, Enrico Schlesinger. 2003-12-19. Monodromy of Projective Curves. https://arxiv.org/abs/math/0312375

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