Samuel Johnston. Birational Invariance in Punctured Log Gromov–Witten Theory. Algebraic Geometry. 2026.
Abstract
Given a log smooth scheme (X, D) and a log \textasciiacute etale modification (X\texttildelow{} , D\texttildelow{} ) {\(\rightarrow\)} (X, D), we relate the punctured Gromov–Witten theory of (X\texttildelow{} , D\texttildelow{} ) to the punctured Gromov–Witten theory of (X, D), generalizing results of Abramovich and Wise in the nonpunctured setting. Using the main comparison results, we show a form of log \textasciiacute etale invariance for the logarithmic mirror algebras and canonical wall structures constructed by Gross and Siebert, respectively.