Questions tagged [pushforward]

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Pushforward of the structure sheaf for smooth morphisms

Let $\pi:X\to S=\mathbb{P}^1_{\mathbb{Z}}$ be a smooth morphism. Is there a smooth separated morphism $\pi':X'\to S$ such that $\pi_*\mathcal{O}_X\approx \pi'_*\mathcal{O}_{X'}$ as $\mathcal{O}_S$-...
3
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0answers
55 views

Relation between the orientation sheaves of the interior and the boundary of a topological manifold

Let $(M, \partial M)$ be an $n$-dimensional topological manifold with boundary. Let $\mathcal{O}_{M \setminus \partial M}$ and $\mathcal{O}_{\partial M}$ denote the orientation sheaves of $M \setminus ...
1
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1answer
117 views

Gysin map for projective sub-bundles of exceptional divisors

Let $X$ be a smooth, projective variety, $Y \subset X$ a smooth, projective subvariety of codimension $3$. Denote by $\pi:\tilde{X} \to X$ the blow-up of $X$ along $Y$ and by $E$ the exceptional ...
4
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1answer
347 views

Pushforward of curves

Let $Z$ be a subvariety of an irreducible projective variety $X$, and let $i:Z\rightarrow X$ be the inclusion. Let $N_1(X),N_1(Z)$ be the $\mathbb{Q}$-vector spaces of curves in $X$ and $Z$ ...
1
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0answers
314 views

Isomorphism of probability spaces

Consider a surjective map $f:(X, \sigma(f)) \to (Y, \mathcal{Y})$, if a measure $\nu$ is given in $(Y, \mathcal{Y})$ the pullback $\nu(f(\cdot))$ is a measure on $(X, \sigma(f))$, similarly if $\mu$ ...
5
votes
1answer
389 views

Pushforward of line bundle under “toric isogeny”

Let $(X,T)$ be a smooth complex toric variety of dimension $d$ with torus $T$ and toric boundary $D=X\setminus T$. Let $\phi : X\to X$ be a finite endomorphism of $X$ such that the restriction $$\phi|...
1
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2answers
564 views

Push-forward of a nef bundle

Let $f:X\rightarrow Y$ be a finite morphism between normal varieties. Let $E$ be a vector bundle on $X$ and let us consider its pushforwad $f_{*}E$. Does anyone know an example where $E$ is nef but $...
22
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3answers
6k views

Pullback measures

Why do all measure theory textbooks present the concept of push-forward measure, but never the concept of pull-back measure? Doesn't the latter exist? It's true that the naive treatment of such a ...
2
votes
2answers
451 views

sheaves for which the derived (compact or not) pushforward is zero

Conventions: sheaf = complex of constructible sheaves (in the l-adic setup with etale tplg or in the complex coefficients setup with analytical tplg). I would like to understand if there is an ...