The intrinsic mirror construction conjecture

About 4 years old · traced to

Let YY be a Fano manifold with smooth anticanonical divisor DD. For a suitable submonoid P⊂Pic⁡(Y)P\subset \operatorname{Pic}(Y), let (X,W)(X,W) be the intrinsic mirror dual, where

X→Spf⁡C[Pic⁡(Y)∗]⟦P⟧X\to \operatorname{Spf}\mathbb{C}[\operatorname{Pic}(Y)^*]\llbracket P\rrbracket

is a formal degenerating family of affine Calabi–Yau manifolds and W∈Γ(X,OX)W\in\Gamma(X,\mathcal{O}_X) is the unique primitive theta function. Intrinsic mirror construction conjecture. The broken line expansion of WW in a chamber of the wall structure near infinity is the open mirror map of KYK_Y. This extends the proper-potential/open-mirror-map relationship to intrinsic mirrors in the non-toric and higher-dimensional settings; the source gives no resolution of the conjecture.

References

Primary source

Tim Gräfnitz, Helge Ruddat and Eric Zaslow, “The proper Landau-Ginzburg potential is the open mirror map”, arXiv:2204.12249 (2024).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.