6
votes
Accepted
A complex version of the Cahiers topos
This has already been done, see the article EFC-algebra and references therein.
In particular, the paper of Pridham constructs the topos of ∞-sheaves on the site of (derived) Stein spaces and explores ...
6
votes
Accepted
Criteria for when Gauss-Manin sheaves are vector bundles
If I am reading the assumptions correctly, this should follow from Theorem 6.4 in the paper
Luc Illusie, Kazuya Kato and Chikara Nakayama
Quasi-unipotent Logarithmic Riemann-Hilbert Correspondences
J. ...
5
votes
Number of regions created by r hyper-planes in n-dimensional space
One proof is in my book Enumerative Combinatorics, vol. 1, second ed., Proposition 3.11.8. The first proof is due to L. Schläfli, written in 1850-52 but not published until 1901 in Neue allgemeinen ...
4
votes
Proving that $H^1(X,\mathcal{Hom}(\mathcal{G},\mathcal{E})) \cong \text{Ext}^1(\mathcal{G},\mathcal{E})$ holds for locally free sheaves
This isomorphism holds for any degree of cohomology and it only requires that the first sheaf $\mathcal{G}$ is locally free. This relies on the fact that $\mathcal{H}om(\mathcal{G},-)$ is exact. There ...
4
votes
Accepted
Gluing local holomorphic connections
(Updated, as I realized the formula stated by Huybrechts indeed also does make sense without making any identifications.)
One should interpret the two sides in the compatibility condition of ...
2
votes
Accepted
Nearby cycles for stacks
I don't know a reference, but let me discuss a strategy for a proof of the comparison that I think should work.
By Artin's comparison, if we take a constant sheaf $\mathbb Z/\ell^n$ and then pull back ...
2
votes
Nearby cycles for stacks
I am not sure about the relation between the algebraic nearby cycles functors (at this point, I believe that the algebraic in your mind is the one in étale cohomology, which is somehow analogous but ...
1
vote
Request for non-Einstein positive constant scalar curvature Kähler surfaces
I unfortunately am not able to comment, so I’ll have to write what I can say here: As you point out, the compact surfaces admitting Kähler metrics of positive Ricci curvature, i.e., Del Pezzo surfaces,...
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