# ag.algebraic geometry – Examples of effectual Lefschetz situation Answer

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ag.algebraic geometry – Examples of effectual Lefschetz situation

When a closed subvariety $$Y$$ of $$X$$ answer effectual Lefschetz situation $$Leff(X,Y)$$, it implies there’s an equivalence if classes between the vector bundles on the formal neighborhood of $$Y$$ in $$X$$ and vector bundles on a neighborhood of $$Y$$. One of functors inducing this equivalence is limpid, it’s the restriction functor which is require. Is there any categorical description of the opposite functor? Is it require?

A theorem Hartshorne implies that when $$X$$ and $$Y$$ are flush projective varieties and $$Y$$ is a whole intersection with $$textual content{dim}(Y)geq 2$$, this property holds. I marvel whether or not there are any attention-grabbing examples of pairs that $$X$$ is a floor and $$Y$$ is a round, I’m extra enthusiastic about having an attention-grabbing $$X$$. (in parch $$p$$ ideally)

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