Zaslow's crepant-resolution conjecture for stringy Hodge numbers

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Let XX be a smooth Calabi–Yau manifold with an action of a finite group HH preserving the holomorphic volume form, let Y=X/HY=X/H, and let hstp,q(Y)h_{st}^{p,q}(Y) denote its stringy Hodge numbers. A resolution Z→X/HZ\to X/H is crepant when its canonical divisor is the pullback of the canonical divisor of X/HX/H. Zaslow's conjecture. If Z→X/HZ\to X/H is any crepant resolution of X/HX/H, then

hp,q(Z)=hstp,q(X/H).h^{p,q}(Z)=h_{st}^{p,q}(X/H).

This conjecture predicts that the stringy Hodge numbers of a quotient agree with the ordinary Hodge numbers of every crepant resolution, generalizing the corresponding equality for stringy and ordinary Euler characteristics. The supplied text gives no resolution status.

References

Primary source

Jim Bryan, Ron Donagi and Naichung Conan Leung, “G-bundles on Abelian surfaces, hyperkahler manifolds, and stringy Hodge numbers”, arXiv:math/0004159 (2000).

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