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H then carries over to any base Field , when Ω is taken to be the sheaf of Kähler Differential s and the power is the (top) Exterior Power . The definition of geometric genus is carried over classically to singular curves ''C'', by decreeing that p is the geometric genus of the Normalization ''C''′. That is, since the mapping C is Birational , the definition is extended by birational invariance. The geometric genus is the first invariant ''p''''g'' = ''P1'' of a sequence of invariants ''Pn'' called the Plurigenera . SEE ALSO |
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