Orbifold–resolution conjecture for BCOV invariants

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Let YY be a Calabi–Yau orbifold and let Y~→Y\widetilde{Y}\to Y be a crepant resolution. Orbifold–resolution conjecture. There is a constant C(Y~/Y)C(\widetilde{Y}/Y), depending only on the topological type of the crepant resolution, such that

τBCOVorb(Y)=C(Y~/Y) τBCOV(Y~).\tau_{\rm BCOV}^{\rm orb}(Y)=C(\widetilde{Y}/Y)\,\tau_{\rm BCOV}(\widetilde{Y}).

This proposes a topological comparison between the orbifold BCOV invariant and the ordinary BCOV invariant after crepant resolution. The source does not state any resolution or partial result for this proposal.

References

Primary source

Ken-Ichi Yoshikawa, “Analytic torsion for Borcea-Voisin threefolds”, arXiv:1410.0212 (2016).

Additional references

2 papers in this index state this conjecture (2010–2014). The statement above is taken from the most recent of them; the others are arXiv:1008.4205.

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