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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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Understanding the picture of monoidal space

Ogus states that he draws a log scheme $(X,\mathcal{M})$ by first drawing $X$ and then adding a picture of $\operatorname{Spec}\mathcal{M}_x$ at each $x\in X.$ (He says this on page 21.) In this case, …
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