Morphism between surfaces

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Suppose that $S$ is a surface of general type. Let $K_S$ the canonical bundle of $S$ and $\phi=\phi_{K_S}$ the canonical map. Suppose that the canonical map is a morphism from $S$ to $\mathbb{P}^{p_g-1}$ of degree 1.
Can i say that $\phi$ is an embedding between $S$ and its image in the projective space?