Orbifold–resolution conjecture for BCOV invariants

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.

Sources & referencesView supporting material

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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