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Behavior of divisors under push forward and pull back

Consider a birational morphism between smooth projective varieties $f:X\to Y$. I would like to understand the behavior of push-pull/pull-push of effective divisors under $f$. I know that if $D$ is an ...
Khainq's user avatar
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1 vote
1 answer
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Push-forward of divisors and intersections

Let $f:X\rightarrow Y$ be a surjective finite morphism of varieties, with $X$ normal and $Y$ smooth. Let $D\subset X$ be a divisor and $C\subset Y$ a curve. Does the equality $$C\cdot f_{*}D = f^{*}C\...
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2 votes
1 answer
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Pushforward of a very ample line bundle on a curve to $\mathbb{P}^1$

Let $p:C\to\mathbb{P}^1$ be a degree $k$ morphism from a smooth projective curve $C$ to the projective line and $L$ a very ample line bundle on $C$. We know that $p_*\mathcal{O}_C(L)$ is a rank $k$ ...
Li Li's user avatar
  • 439