Encyclopedia > G > Geometric genus
Geometric genus
In mathematics, the geometric genus in algebraic geometry is a basic birational invariant pg of algebraic varieties, defined for non-singular complex projective varieties (and more generally for complex manifolds) as the Hodge number hn,0 (equal to h0,n by Serre duality). In other words for a variety V of complex dimension n it is the number of linearly independent holomorphic n-forms to be found on V.
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