The intrinsic mirror construction conjecture

From papers

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

XSpfC[Pic(Y)]PX\to \operatorname{Spf}\mathbb{C}[\operatorname{Pic}(Y)^*]\llbracket P\rrbracket

is a formal degenerating family of affine Calabi–Yau manifolds and WΓ(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.

Progress summary

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

Sources & referencesView supporting material

Primary source

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

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