Type: Article

A family of plane curves with moduli 3g-4

Abel Castorena;

Abstract:

In the moduli space M(g) of smooth and complex irreducible projective curves of genus g, let GP(g) be the locus of curves that do not satisfy the Gieseker-Petri theorem. Let GP(g,d)(1) be the subvariety of GPg formed by curves C of genus g with a pencil g(d)(1) = (V, L) is an element of G(d)(1)(C) free of base points for which the Petri map mu(V): V circle times H(0)(C, K(C) circle times L(-1)) -> H(0)(C, K(C)) is not injective. For g >= 8, we construct in this work a family of irreducible plane curves of genus g with moduli 3g - 4 in GP(g,g-2)(1).