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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory
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Is $(x^2y,xy^2)$ log smooth?
Warning: I'm not an expert on logarithmic geometry.
According to Proposition 4.1.2. of Ogus' Lectures on Logarithmic Algebraic Geometry, a log smooth morphism (of fine log schemes) is log flat. Log fl …