Definition 33.45.10. Let $k$ be a field. Let $X$ be a proper scheme over $k$. Let $\mathcal{L}$ be an ample invertible $\mathcal{O}_ X$-module. For any closed subscheme the degree of $Z$ with respect to $\mathcal{L}$, denoted $\deg _\mathcal {L}(Z)$, is the intersection number $(\mathcal{L}^ d \cdot Z)$ where $d = \dim (Z)$.

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