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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