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A Hartogs-type criterion for flatness

Let $U$ be a smooth affine connected variety over $\mathbb C$ and let $V\subset U$ be an open whose complement is of codimension at least two. Now, let $Y$ be a smooth quasi-affine connected variety ...
Christophe's user avatar
2 votes
0 answers
198 views

Proposition 4.3.8 Qing Liu about flat morphisms of schemes

I have a problem with a detail of Qing Liu's proof of Proposition 4.3.8 (pag. 137 of "Algebraic Geometry and Arithmetic Curves"). The statement is: Let $Y$ be a scheme having only a finite ...
BernyPiffaro's user avatar
1 vote
0 answers
135 views

Projection from closure of locally closed subscheme is Etale

Let $S$ an arbitrary scheme and denote by $\Delta: S \to S \times S$ the diagonal immersion and $p_i: S \times S \to S$ the both projections to first resp second factor. (in following we will wlog ...
user267839's user avatar
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0 votes
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276 views

Flatness of affine cone due to semicontinuity theorem

I would like to clarify an important aspect from the discussion in this question. The OP discussed an obstacle to solve part (c) from Exercise 9.5 from Hartshorne's Algebraic Geometry Chap. III page ...
user267839's user avatar
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0 votes
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89 views

Locally freeness of twisted direct images $\pi_* \mathcal{F}(i)$

I have a question about a step in the proof of the Existence of Flattening Stratification I found in Nitsure's paper here: https://arxiv.org/abs/math/0504590 This question is closely related to Local ...
user267839's user avatar
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