Plasma acceleration

In mathematics, the arithmetic genus of an algebraic variety is one of some possible generalizations of the genus of an algebraic curve or Riemann surface.

The arithmetic genus of a complex projective manifold of dimension n can be defined as a combination of Hodge numbers, namely

p_a = h^n,0 − h^{n − 1, 0} + ... + (−1)^{n − 1}h^{1, 0}.

When n = 1 we have χ = 1 − g where g is the usual (topological) meaning of genus of a surface, so the definitions are compatible.

By using h^p,q = h^q,p for compact Kähler manifolds this can be reformulated as the Euler characteristic in coherent cohomology for the structure sheaf ${\mathcal{𝒪}}_M$:

$p_a=(-1{)}^n(\chi ({\mathcal{𝒪}}_M)-1).$

This definition therefore can be applied to some other locally ringed spaces.

See also

• Genus (mathematics)
• Geometric genus

References

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Further reading

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534