Geodesic
Quantum cohomology of the Hilbert scheme of points on 𝒜_{𝓃}-resolutions
Maulik, Davesh1 ; Oblomkov, Alexei2
1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
2 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Journal of the American Mathematical Society, Tome 22 (2009) no. 4, pp. 1055-1091

Voir la notice de l'article provenant de la source American Mathematical Society

We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type $A_{n}$ singularities. The operators encoding these invariants are expressed in terms of the action of the the affine Lie algebra $\widehat {\mathfrak {gl}}(n+1)$ on its basic representation. Assuming a certain nondegeneracy conjecture, these operators determine the full structure of the quantum cohomology ring. A relationship is proven between the quantum cohomology and Gromov-Witten/Donaldson-Thomas theories of $A_{n}\times \mathbf {P}^1$. We close with a discussion of the monodromy properties of the associated quantum differential equation and a generalization to singularities of types $D$ and $E$.
DOI : 10.1090/S0894-0347-09-00632-8

Maulik, Davesh 1 ; Oblomkov, Alexei 2

1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
2 Department of Mathematics, Princeton University, Princeton, New Jersey 08544 
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Maulik, Davesh; Oblomkov, Alexei. Quantum cohomology of the Hilbert scheme of points on 𝒜_{𝓃}-resolutions. Journal of the American Mathematical Society, Tome 22 (2009) no. 4, pp. 1055-1091. doi: 10.1090/S0894-0347-09-00632-8

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