Questions tagged [gromov-witten-theory]
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163 questions
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Why would I want to know (equivariant) quantum cohomology?
Let's say that I have a variety I think is interesting, and based on some papers I don't fully understand, I can compute quite explicitly its equivariant quantum cohomology in terms of explicit ...
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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 ...
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GW invariants for varieties with negative first Chern class
Does there exist any theorem claiming that if a variety with negative first Chern class has no rational curves then every GW invariant is zero?
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Convergence of quantum cohomology
For which manifolds or varieties is quantum cohomology known to converge? Are there any manifolds for which quantum cohomology is known to not converge? I seem to have the impression that quantum ...
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References for Donaldson-Thomas theory and Pandharipande-Thomas theory?
I'm looking for good introductory references for Donaldson-Thomas theory and Pandharipande-Thomas theory. I know a bit about Gromov-Witten theory, but almost nothing about Donaldson-Thomas and ...
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Higher-dimensional Gromov-Witten theories
A basic set-up in modern enumerative geometry is that you have some object $X$ (say, a "nice" stack, for whatever definition of "nice" you need) and then you want to "count&...
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Higher genus closed string B-model
The closed string A-model is mathematically described by Gromov-Witten invariants of a compact symplectic manifold $X$. The genus 0 GW invariants give the structure of quantum cohomology of $X$, which ...
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a question about Gromov-Witten invariant
Do the Gromov-Witten invariants count the morphisms from a curve to a variety over $\mathbb{C}$?
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Negative Gromov-Witten invariants
I understand the heuristic reason why Gromov-Witten invariants can be rational; roughly it's because we're doing curve counts in some stacky sense, so each curve $C$ contributes $1/|\text{Aut}(C)|$ to ...
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Picard-Fuchs equations
If I have the periods $$\pi_1(\lambda)=\int_0^1\frac{dx}{\sqrt{x(x-1)(x-\lambda)}}$$ and $\pi_2(\lambda)$ similarly defined of the cubic curve $$y^2z=z(x-z)(x-\lambda z)$$ Such functions will be ...
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What are Gromov-Witten invariants in terms of physics?
What do Gromov-Witten invariants (of say a Calabi-Yau 3-fold) represent, or what are they supposed to represent, in terms of string theory? When I compute GW invariants, am I actually computing some ...
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Manifolds distinguished by Gromov-Witten invariants?
What is a simplest example of a manifold $M^{2n}$ that admits two symplectic structures with isotopic almost complex structures, and such that Gromov-Witten invariants of these symplectic structures ...
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Gromov-Witten theory and compactifications of the moduli of curves
Why, from a string theory perspective, is it natural to consider the Deligne-Mumford (resp. Kontsevich) compactification of the moduli of curves (resp. maps [from curves to a target space X]) rather ...
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