All Questions
Tagged with deformation-theory cohomology
7 questions
8
votes
1
answer
405
views
Deformations of Vertex Algebras
As the title suggests, I'm interested in deformation theory of vertex algebras and their representations.
In the paper https://arxiv.org/abs/1806.08754, the authors construct, for a vertex algebra $...
user108998
5
votes
0
answers
197
views
Torsion-free sheaf cohomology over discrete valuation rings
Let $R$ be a Henselian discrete valuation rings with algebraically closed residue field and $X$ be a regular, flat, proper $R$-scheme. Assume that the generic fiber to the natural morphism from $X$ to ...
- 2,126
2
votes
0
answers
266
views
Deformations of associative algebras and Hochschild cohomology
I am studying the deformation theory of associative algebras (and Poisson algebras) and came across a question for which I cannot find an answer:
Let $(A,\mu)$ be a commutative associative algebra ...
- 491
11
votes
2
answers
780
views
Deformations of a blowup
Let $S$ be a smooth projective surface over $\mathbb{C}$. (I guess this can be more general—higher dimension, other ground fields, non-projective, maybe even singular?—and I'dd like to hear that.) Let ...
- 5,504
3
votes
0
answers
175
views
Cycle class map in non-smooth family of projective varieties
Let $\pi:\mathcal{X} \to T$ be a family of smooth projective complex varieties. Assume $T$ is quasi-projective, reduced, irreducible but not smooth and of positive dimension. Let $\mathcal{Z}$ be a ...
- 833
10
votes
2
answers
2k
views
A simple proof of the Weyl algebra's rigidity.
I am wondering if there is a nice presentation of the Hochschild cohomology of $A_n$ the Weyl algebra. It is known that $H^m(A_n,A_n)=0$ for $m>0$, and thus it is rigid. A proof can be found in ...
- 4,842
9
votes
1
answer
443
views
Reverse Engineering to find deformation problem (from cohomology groups)?
One of my favorite explanation of the cohomology groups of low degree is that they arise as the automorphism group, tangent space and obstruction space (or where the obstruction lives) of a certain ...
- 5,052