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Let $X, Y$ be two projective schemes contained in $\mathbb{P}^n$ for some $n$. Let $f:X \to Y$ be a surjective projective morphism between smooth projective varieties over $\mathbb{C}$. Under what condition on $f$ can we conclude that the degree of $X$ is equal to the degree of $Y$ added to the degree of the generic fiber of $f$?

Let $i_1:X \hookrightarrow \mathbb{P}^n$ and $i_2:Y \hookrightarrow \mathbb{P}^N$ be two projective schemes. Let $f:X \to Y$ be a surjective projective morphism between smooth projective varieties over $\mathbb{C}$. Denote by $g$ the composition of $f$ with $i_2$. Under what condition on $g$ can we conclude that the degree of $X$ is equal to the degree of $Y$ in $\mathbb{P}^N$ added to the degree of the generic fiber of $g$?

Let $f:X \to Y$ be a surjective projective morphism between smooth projective varieties over $\mathbb{C}$. Under what condition on $f$ can we conclude that the degree of $X$ is equal to the degree of $Y$ added to the degree of the generic fiber of $f$?

Let $X, Y$ be two projective schemes contained in $\mathbb{P}^n$ for some $n$. Let $f:X \to Y$ be a surjective projective morphism between smooth projective varieties over $\mathbb{C}$. Under what condition on $f$ can we conclude that the degree of $X$ is equal to the degree of $Y$ added to the degree of the generic fiber of $f$?

Let $f:X \to Y$ be a projective morphism between smooth projective varieties over $\mathbb{C}$. Under what condition on $f$ can we conclude that the degree of $X$ is equal to the degree of $Y$ added to the degree of the generic fiber of $f$?

Let $f:X \to Y$ be a surjective projective morphism between smooth projective varieties over $\mathbb{C}$. Under what condition on $f$ can we conclude that the degree of $X$ is equal to the degree of $Y$ added to the degree of the generic fiber of $f$?