Some remarks on the schemesW
d
r |
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Authors: | Marc Coppens |
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Institution: | (1) Present address: Katholieke Industriële Hogeschool der Kempen, Campus H. I. Kempen Kleinhoefstraat 4, B 2440 Geel, Belgium |
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Abstract: | Summary Let X be an irreducible smooth projective curve of genus g. Let
d
r
(g) be the Brill-Noether Number. In this paper we prove some results concerning the schemes W
d
r
of special divisors. 1) Suppose dim (W
d–1
r
)=
d– 1
r
(g)0 and
d
r
(g) < g. If W
d– 1
r
is a reduced (resp. irreducible) scheme, then W
d
r
is a reduced (resp. irreducible) scheme. 2) Under certain conditions, if Z is a generically reduced irreducible component of W
d–1
r
then Z W
1
0
is a generically reduced irreducible component of W
d
r
. 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
d
1
. |
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Keywords: | |
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