All Questions
Tagged with deformation-theory sg.symplectic-geometry
9 questions
7
votes
1
answer
679
views
Relation between symplectic (co)homology and Hochschild (co)homology and deformations
A very fluffy question in which I'm ignorant of homology/cohomology, grading etc:
The open-closed and closed-open string maps relating the symplectic (co)homology and Hochschild (co)homology of the ...
- 73
7
votes
0
answers
139
views
Could we extend the star product on a Poisson manifold from its ring of smooth functions to its de Rham complex?
Let $M$ be a smooth manifold with a Poisson bracket $\{-,-\}$. Kontsevich proved that there exists a deformation quantization of $M$, i.e. let $C^{\infty}(M)[[\hbar]]=C^{\infty}(M)\otimes_{\mathbb{R}}\...
- 9,019
1
vote
0
answers
141
views
Constructing embedded families of curves with general moduli
Is there a known way to construct flat families of smooth curves $\mathcal{C}/\mathcal{B}$ which are fiberwise embedded in a family of projective varieties $\mathcal{X}/\mathcal{B}$ and which have ...
- 1,981
6
votes
1
answer
288
views
Deformation long exact sequence of GW theory in the analytical setting
Let $f\!=\!(u\colon (\Sigma,p_1,\ldots,p_k) \to X)$ be an element of the moduli space of genus $g$ $k$-marked degree $A$ $J$-holomorphic maps $\mathcal{M}_{g,k}(X,A,J)$. For simplicity assume $C=(\...
7
votes
1
answer
1k
views
What's the relation between the heat kernel proof of the index theorem and deformation quantization?
In the book "Heat kernels and Dirac operators", I found the slogan by Quillen in the Introduction: "Dirac operators are a quantization of the theory of connections, and the supertrace of the heat ...
- 9,019
10
votes
3
answers
2k
views
In the dictionary between Poisson and Quantum, what corresponds to Coisotropic?
I work entirely over a field of characteristic $0$, in case it matters.
Recall that a Poisson algebra is a commutative algebra $A$ with a bracket $\lbrace,\rbrace : A^{\wedge 2} \to A$ which is (1) a ...
- 54.6k
8
votes
1
answer
469
views
Looking for a particular family of C.Y quintics
It is possible to construct (in many ways) a family of Calabi-Yau quintics $\mathcal{X}\rightarrow \Delta$, over disk, such that the fiber over $0$ has a singularities locally given by the equation $...
2
votes
0
answers
365
views
Are schematic fixed points of a torus action on an affinized twistor deformation flat?
This is a follow-up to some earlier questions about flatness of schematic fixed points of certain deformations. Since I could never come up with good enough hypotheses in those examples, let me try a ...
- 44.7k
11
votes
1
answer
1k
views
Is the generic deformation of a symplectic variety affine?
Kaledin and Verbitsky have shown that symplectic varities have a remarkably nice deformation theory as symplectic varieties.
Let $X$ be a symplectic variety (a smooth quasi-projective variety over $\...
- 44.7k