ScalingStacks

Conjecture 3.31 . [04BR]

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Conjecture 3.31.

Suppose we have almost calibrated exact Lagrangian objects L1,L2,LL_{1},L_{2},L, fitting into a distinguished triangle L1→L→L2→L1​[1]L_{1}\to L\to L_{2}\to L_{1}[1], and satisfies the destabilizing condition

θ^1=arg∫L1Ω>θ^2=arg∫L2Ω.\hat{\theta}_{1}=\arg\int_{L_{1}}\Omega>\hat{\theta}_{2}=\arg\int_{L_{2}}\Omega.

Then the phase angle inequality (31) follows. In particular, the derived category class of LL admits no special Lagrangian representative.

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