Summary
Let X be an irreducible smooth projective curve of genus g. Let ϱ rd (g) be the Brill-Noether Number. In this paper we prove some results concerning the schemes W rd of special divisors. 1) Suppose dim (W rd−1 )=ϱ rd− 1 (g)⩾0 and ϱ rd (g) < g. If W rd− 1 is a reduced (resp. irreducible) scheme, then W rd is a reduced (resp. irreducible) scheme. 2) Under certain conditions, if Z is a generically reduced irreducible component of W rd−1 then Z ⊕ W 01 is a generically reduced irreducible component of W rd . 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 W 1d .
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Coppens, M. Some remarks on the schemesW r d . Annali di Matematica pura ed applicata 157, 183–197 (1990). https://doi.org/10.1007/BF01765318
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DOI: https://doi.org/10.1007/BF01765318