Auroux's boundary conjecture for special Lagrangian torus fibrations

Let XX be a variety with a smooth anticanonical divisor DD, set U=XDU=X\setminus D, and let π:UB\pi:U\to B be a special Lagrangian torus fibration, meaning that its smooth fibers are special Lagrangian tori. Auroux's boundary conjecture. Near the divisor DD, the special Lagrangian torus fibers of π\pi are S1S^1-bundles over a special Lagrangian torus fiber of a special Lagrangian torus fibration on DD. This describes the expected boundary behavior underlying the SYZ construction of the mirror and is attributed in the source to Auroux's Conjecture 7.3.

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Primary source

Andrew Harder, Ludmil Katzarkov and Victor Przyjalkowski, “P=W Phenomena”, arXiv:1905.08706 (2019).

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