Birational Invariance in Punctured Log Gromov-Witten Theory

Abstract

Given a log smooth scheme $(X,D)$, and a log étale modification $(\tilde{X},\tilde{D})\to (X,D)$, 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 étale 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.

arXiv comment44 pages. To appear in Algebraic Geometry