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arithmetic genus
The arithmetic genus of a projective variety \(\mathrm{X}\) of dimension \(r\) is \((-1)^{r}\left(\chi\left(\mathcal{O}_{X}\right)-1\right)\).
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The arithmetic genus of a projective variety \(\mathrm{X}\) of dimension \(r\) is \((-1)^{r}\left(\chi\left(\mathcal{O}_{X}\right)-1\right)\).