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Results tagged with coherent-sheaves
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user 108274
13
votes
2
answers
3k
views
Sheaf of relative Kähler differentials intuitively
Let $f: X \to Y$ be a separated morphism between $k$-varieties or more general schemes
of finite type. The most common way in standard literature on algebraic
geometry to define the sheaf of relative …
- 6,018
4
votes
1
answer
288
views
Yoga on coherent flat sheaves $\mathcal{F}$ over projective space $\mathbb{P}^n$
I'm reading Mumfords's Lectures on Curves on an Algebraic Surface (jstor-link: https://www.jstor.org/stable/j.ctt1b9x2g3)
and I found in Lecture 7 (RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON
$\ma …
- 6,018
2
votes
Sheaf of relative Kähler differentials intuitively
supplement/ an "almost" answer: I noticed that OP's of several related questions (1, 2) asked about similar
issue. The best explanation I found there was that for a smooth manifold $X$
the tangent spa …
- 6,018
2
votes
0
answers
142
views
Local freeness of $\pi_*F(r)$ from flatness of $F$
In 'Fundamental Algebraic Geometry' by Fantechi there is a lemma in section 5.3.2, page 119:
LEMMA 5.5 Let $S$ be a noetherian scheme and let $F$ be a coherent sheaf on $\mathbb{P}^n_S$. Suppose there …
- 6,018
1
vote
0
answers
261
views
Devissage lemma (Mumford's & Oda's AG II)
This question is part II of my proof reading of Lemma of devissage
from Mumford's & Oda's Algebraic Geometry II, findable on page 81; Theorem 6.12:
Theorem 6.12 (“Lemma of devissage”). Let $K$ b …
- 6,018
0
votes
0
answers
153
views
Hyperplane which does not contain any associated point of qc sheaf $\mathcal{F}$
I have a question about an argument on $m$-regularity
from 'Fundamental Algebraic Geometry' by Fantechi on page 114, Chapter
5.2: Castelnovo-Mumford regularity. The statement is:
Let $k$ be a field a …
- 6,018
0
votes
0
answers
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 …
- 6,018
0
votes
0
answers
214
views
Use of flattening stratification (from Nitsure's construction of Hilbert and Quot schemes)
I study Nitin Nitsures paper on the Construction of Hilbert and Quot Schemes and not understand the propetry (F) completely:
In previous chapter (Embedding Quot into Grassmanian) it was
proved that t …
- 6,018