Exercise 111.59.6. Let $k$ be an algebraically closed field. Let $g \geq 3$. Let $X$ and $X'$ be smooth projective curves over $k$ of genus $g$ and $g + 1$. Let $Y \subset X \times X'$ be a curve such that the projections $Y \to X$ and $Y \to X'$ are nonconstant. Prove that the nonsingular projective model of $Y$ has genus $\geq 2g + 1$.
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