| Version 4 |
Version 3 |
| The {\em genus} of a smooth projective curve $X$ over a field $k$ is the |
The {\em genus} of a smooth projective curve $X$ over a field $k$ is the rank |
| dimension over $k$ of the vector space $\Omega^1(X)$ of global regular |
over $k$ of the vector space $\Omega^1(X)$ of global regular differentials on $X$. |
| differentials on $X$. |
|
| The genus is a birational invariant. |
The genus is a birational invariant. |
