In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface. == Projective varieties == Let X be a projective scheme of dimension r over a field k, the arithmetic genus p a {\displaystyle p_{a}} of X is defined as p a ( X ) = ( − 1 ) r ( χ ( O X ) − 1 ) .
In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface. == Projective varieties == Let X be a projective scheme of dimension r over a field k, the arithmetic genus p a {\displaystyle p_{a}} of X is defined as p a ( X ) = ( − 1 ) r ( χ ( O X ) − 1 ) .
Source: Wikipedia "Arithmetic genus" · CC BY-SA 4.0
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