For special toric degenerations of K3 surfaces, the intrinsic mirror and the universal toric degeneration mirror coincide after restricting to the minimal relative Gross-Siebert locus and basechanging by the polarization.
Birational Invariance in Punctured Log Gromov-Witten Theory
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abstract
Given a log smooth scheme $(X,D)$, and a log \'etale modification $(\tilde{X},\tilde{D}) \rightarrow (X,D)$, we relate the punctured Gromov-Witten theory of $(\tilde{X},\tilde{D})$ to the punctured Gromov-Witten theory of $(X,D)$, generalizing results of Abramovich and Wise in the non-punctured setting in "Birational invariance in log Gromov-Witten Theory". Using the main comparison results, we show a form of log \'etale invariance for the logarithmic mirror algebras and canonical scattering diagrams constructed in "Intrinsic Mirror Symmetry" and "The Canonical Wall Structure and Intrinsic Mirror Symmetry" respectively.
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Mirrors to toric degenerations via intrinsic mirror symmetry
For special toric degenerations of K3 surfaces, the intrinsic mirror and the universal toric degeneration mirror coincide after restricting to the minimal relative Gross-Siebert locus and basechanging by the polarization.