Smooth projective curve/Locally free sheaf/Degree/Definition

Degree of a locally free sheaf on a curve

Let ${}C$ denote a smooth projective curve over an algebraically closed field ${}K$. For a locally free sheaf ${}{\mathcal {G}}$ on ${}C$ of rank ${}r$ we define its degree by the degree of the determinant sheaf ${}\bigwedge ^{r}{\mathcal {G}}$.