All Questions
Tagged with ag.algebraic-geometry fukaya-category
8 questions
20
votes
1
answer
4k
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Hochschild (co)homology of Fukaya categories and (quantum) (co)homology
There is a conjecture of Kontsevich which states that Hochschild (co)homology of the Fukaya category of a compact symplectic manifold $X$ is the (co)homology of the manifold. (See page 18 of ...
- 21k
16
votes
2
answers
2k
views
Deformation quantization and quantum cohomology (or Fukaya category) -- are they related?
Good afternoon.
Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "...
- 21k
11
votes
1
answer
2k
views
"Fourier-Mukai" functors for Fukaya categories?
I just skimmed a bit of this fresh-off-the-press paper on homological mirror symmetry for general type varieties.
One thing that intrigued me was statement (ii) of Conjecture 3.3. It suggests that, ...
- 21k
10
votes
2
answers
1k
views
Fukaya categories of hyperkahler reductions: general request for information
I'd really like to hear any references or information people have about the Fukaya categories of hyperkahler reductions of vector spaces (for more informations on the varieties, see Nick Proudfoot's ...
- 44.7k
9
votes
0
answers
629
views
Orlov equivalence between Fukaya categories
In his famous paper https://arxiv.org/abs/math/0503632, Orlov proves the following theorem (for simplicity, let's just focus on the Calabi-Yau case)
Theorem(Orlov): Suppose that $W: \mathbb{A}^d \...
- 915
6
votes
0
answers
184
views
Mirror of the autoequivalences of the derived category of del Pezzo surface?
One version of the homological mirror symmetry conjecture states that for every Fano variety $X$ there exists a Landau--Ginzburg model $W$ such that the category of B-branes on $X$ (i.e. the bounded ...
user74900
3
votes
0
answers
308
views
Algebraic Fukaya categories and mirror symmetry
Dominic Joyce and collaborators have outlined a programme to construct algebraic Fukaya categories on an algebraic symplectic manifold (“Fukaya categories” of complex Lagrangians in complex symplectic ...
- 163
2
votes
1
answer
122
views
Bridgeland stability to Fukaya stability on elliptic curve; geometric proof of no slope decreasing homs
For a bridgeland stability condition $(P,Z)$ on $\mathcal{C}$ and $a > b$ we know that $Hom^0(A,B)=0$ for $A,B \in P(a), P(b)$ respectively.
I would like to see the geometric incarnation of this ...
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