Regularity conjecture for the equivariant asymptotic solution

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Let Rστ(n)(t,λ)R_{\sigma\tau}^{(n)}(t,\lambda) be the coefficient of ℏn\hbar^n in the asymptotic solution matrix Rστ(t,λ,ℏ)R_{\sigma\tau}(t,\lambda,\hbar) of the equivariant quantum differential equation, normalized by the stated classical-limit condition. Let λ=0\lambda=0 be the non-equivariant limit, and let tt be a semisimple point of the non-equivariant theory. Regularity conjecture for the equivariant asymptotic solution. If the non-equivariant quantum cohomology is generically semisimple, then Rστ(n)(t,λ)R_{\sigma\tau}^{(n)}(t,\lambda) is regular at λ=0\lambda=0 for such a point tt. The conjecture is stated after the canonical-coordinate regularity conjecture and is later asserted to hold for toric varieties using the equivariant mirror.

References

Primary source

Hiroshi Iritani, “Convergence of quantum cohomology by quantum Lefschetz”, arXiv:math/0506236 (2006).

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