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5 votes
1 answer
759 views

When is the flatness locus non-empty

Under what additional condition on $f$ (other than flatness/ generic flatness) does there exist a non-empty open set $U$ of $X$ such that $f|_U$ is flat? …
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  • 833
5 votes
1 answer
392 views

Covering of schemes and flatness

Let $f:X \to Y$ be a finite surjective morphism of quasi-projective schemes over $\mathbb{C}$, $X$ is reduced and $Y$ is integral. Suppose that there exists an integer $n$ such that for every closed p …
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  • 833
2 votes
0 answers
286 views

$\delta$-functor and commutativity of pull-back with right derivation

Let $f:X \to Y$ be a faithfully flat projective morphism of noetherial $\mathbb{C}$-schemes. Assume that $Y$ is affine, smooth over $\mathbb{C}$. Let $y \in Y$ be a closed point with residue field, sa …
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  • 833