14
P. A. GRIFFITH S
Summarizing:
(1.38) / / we define the Brill-No ether number
(1.39) P = £ - ( r + l)(g-d + r)
then (every irreducible component of) W
d
satisfies
(1.40) di m W r
d
p.
These considerations, together wit h th e examinatio n o f numerous example s (o f whic h
a few are give n at th e en d o f § 2 below ) leads one to suspec t that , if p 0 then : (i ) fo r an y
curve W
d
i s nonempty s o that (1.40) is valid, and (ii ) fo r a general curv e equalit y holds. I n
particular, if p 0 the n o n a general curv e W
r
d
wil l be empty . W e shall discus s these matter s
in § 2 below .
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