All Questions
Tagged with fukaya-category mirror-symmetry
12 questions
3
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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
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1
answer
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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 ...
- 303
13
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3
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Geometric Langlands: From D-mod to Fukaya
This post is rather wordy and speculative, but I promise there is a concrete question embedded within. For experts, I'll open with a question:
Question: Given a compact Riemann surface $X$, why ...
- 3,020
3
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Organizing mirror pairs
At a maximally vague and naive level, mirror symmetry asks the following question: given a complex manifold $(X, I)$, is there a symplectic manifold $(M, \omega)$ and an equivalence between the ...
- 3,020
4
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Comparing different approaches to HMS for elliptic curves
I am trying to understand homological mirror symmetry for elliptic curves from the article of Zaslow-Polishchuk and from Section 6 of the article of Abouzaid and Smith on homological mirror symmetry ...
- 431
4
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1
answer
337
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Mirror symmetry for singular Lagrangian torus fibrations
Let $X$ be a closed symplectic manifold equipped with a smooth Lagrangian torus fibration $\pi:X \rightarrow Q$. Assume that $\pi$ admits a Lagrangian section. By work of Kontsevich-Soibelman, one can ...
- 31
6
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0
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184
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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
18
votes
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What is the Hochschild cohomology of the Fukaya-Seidel category?
Let $(Y, \omega)$ be a compact symplectic manifold and let $Fuk(X,\omega)$ be its Fukaya category. The Hochschild cohomology of this category should be given by $HH^\bullet(Fuk(Y,\omega))=H^\bullet(Y, ...
- 6,920
13
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1
answer
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Wrapped Fukaya categories of Stein manifolds
By the work of Abouzaid, we know that the wrapped Fukaya category of $T^\ast Q$ with $Q$ a closed smooth manifold is generated by a cotangent fiber. Basically, this is an application of Abouzaid's ...
- 3,187
9
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2
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Hochschild homology of Fukaya category in mirror symmetry
Hi
Can one explain to me what is the Hochschild homology of Fukaya category?
I mean the definition.
You can use the notations of FOOO (Fukaya-Oh-Ono-Ohta) if it helps you to explain easier.
I know ...
11
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1
answer
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"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
25
votes
4
answers
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Is the Fukaya category "defined"?
Sometimes people say that the Fukaya category is "not yet defined" in general.
What is meant by such a statement? (If it simplifies things, let's just stick with Fukaya categories of compact ...
- 21k