Questions tagged [quantum-cohomology]
The quantum-cohomology tag has no usage guidance.
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Uniqueness in Mare combinatorics and bounds on Gromov-Witten invariants
Let $R$ be the root system of a Weyl group $W$. Let $\tilde{R}^+$ be the set of $B$-cosmall roots, i.e. the set of positive roots $\alpha$ such that $\ell(s_\alpha)=2\operatorname{ht}\alpha-1$. Based ...
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Quantum cup product and Dolbeault cohomology
Let $X$ be a smooth projective variety over $\mathbb{C}$. We consider the small quantum cup product $\star$ on the deRham cohomology ring $\displaystyle H^*(X;\mathbb{C})=\bigoplus_{p,q}H^{p,q}(X)$. ...
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Equivariant quantum cohomology of conical symplectic resolutions
There is a couple of papers on this [Braverman, Maulik, Oblomkov, Okounkov, Pandharipande] where authors calculate quantum cohomology for various conical symplectic resolutions. The language in these ...
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Can we see the symmetry of the quantum Schubert polynomial of a point
Let $X=G/B$ be a homogeneous space and consider the quantization map
$$
S_W\otimes\mathbb{C}[q]\to(S(\mathfrak{h})\otimes\mathbb{C}[q])/I_W^q\,,
$$
where
$S_W$ is the coinvariant algebra of the Weyl ...
3
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Quantum Cohomology of fiber products
It is well known that the (small) quantum cohomology of a product of two varieties $X$ and $Y$ is given by the tensor product
\begin{equation}QH^\bullet(X)\otimes QH^\bullet(Y).
\end{equation}
This ...
1
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141
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On the maximal powers of $q$ which arise in a quantum product
Let $X=G/P$ be a generalized flag variety (where $G$ denotes a connected, simply connected, semisimple complex linear algebraic group and $P$ a parabolic subgroup). In this paper by Fulton and ...
14
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Why should intersection cohomology and quantum cohomology be related for a symplectic resolution?
In http://arxiv.org/pdf/1410.6240.pdf M. McBreen and N. Proudfoot conjectured a precise relationship between the quantum cohomology of a symplectic resolution and the intersection cohomology of the ...
3
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J-function of cotangent bundle of complete flag variety
Givental and Kim showed that the $J$-function of the complete flag variety $Fl_n=SL_{n}/B$ becomes an eigenfunction of the Toda Hamiltonian. How about the $J$-function of the cotangent bundle $T^*...
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Intuition behind the age grading in quantum cohomology of orbifolds
Let $\mathscr{X}$ be a smooth DM-stack with projective coarse moduli space. I am interested in the orbifold cohomology ring $H^\mathrm{orb}(\mathscr{X})$, as defined by Chen-Ruan (for orbifolds) and ...
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Quantum cohomology of partial flag manifolds
Is there a place in the literature where the quantum differential
equation (or even just quantum cohomology algebra)
of partial flag manifolds $G/P$ is computed for arbitrary semi-simple $G$ and
...