Irreducibility of some families of linear series with Brill-Noether number. I

@inproceedings{LNS2003IrreducibilityOS,
  title={Irreducibility of some families of linear series with Brill-Noether number. I},
  author={SCIENTIFIQUES DE L’{\'E}.N.S and David Eisenbud and Joe P Harris},
  year={2003}
}
— In this paper we study families of linear series of dimension r and degree d on curves of genus g with negative Brill-Noether number P=g-(r+i)(g-d+r) and, allowing specified ramification at a point, on smooth pointed curves. In particular, if p = — 1 we prove that there is exactly one irreducible family of curves and linear series whose curves vary in codimension 1 in the family of all smooth curves. Thus there is at most one component of the Hilbert scheme of nondegenerate smooth curves of… CONTINUE READING
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