In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds. == Definition == The geometric genus can be defined for non-singular complex projective varieties and more generally for complex manifolds of dimension n as the Hodge number hn,0 (equal to h0,n by Serre duality), that is, the dimension of the canonical linear system plus one.
In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds. == Definition == The geometric genus can be defined for non-singular complex projective varieties and more generally for complex manifolds of dimension n as the Hodge number hn,0 (equal to h0,n by Serre duality), that is, the dimension of the canonical linear system plus one.
Source: Wikipedia "Geometric genus" · CC BY-SA 4.0
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