Annali di Matematica Pura ed Applicata

, Volume 157, Issue 1, pp 183–197

Some remarks on the schemesWdr

  • Marc Coppens

DOI: 10.1007/BF01765318

Cite this article as:
Coppens, M. Annali di Matematica pura ed applicata (1990) 157: 183. doi:10.1007/BF01765318


Let X be an irreducible smooth projective curve of genus g. Let ϱdr(g) be the Brill-Noether Number. In this paper we prove some results concerning the schemes Wdr of special divisors. 1) Suppose dim (Wd−1r)=ϱd− 1r(g)⩾0 and ϱdr(g) < g. If Wd− 1r is a reduced (resp. irreducible) scheme, then Wdr is a reduced (resp. irreducible) scheme. 2) Under certain conditions, if Z is a generically reduced irreducible component of Wd−1r then Z ⊕ W10 is a generically reduced irreducible component of Wdr. For r=1, we obtain some further results in this direction. 3) As an application of it we are able to prove some dimension theorems for the schemes Wd1.

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1990

Authors and Affiliations

  • Marc Coppens
    • 1
  1. 1.Katholieke Industriële Hogeschool der KempenGeelBelgium

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