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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory

2 votes
0 answers
240 views

Terminology in log geometry

A log scheme consists of a scheme $X$, a sheaf of monoids $M_X$ on $X$, and a map $\alpha:M_X\to\mathcal O_X$ with the property that $\alpha^{-1}(\mathcal O_X^\times)\to\mathcal O_X^\times$ is an isom …
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7 votes
2 answers
621 views

Is $(x^2y,xy^2)$ log smooth?

Consider the map $$f:\mathbb C^2\to\mathbb C^2$$ $$(x,y)\mapsto(x^2y,xy^2)$$ We can view $f$ as induced by the map of monoids $g:\mathbb Z^2_{\geq 0}\to\mathbb Z^2_{\geq 0}$ given by the matrix $(\beg …
John Pardon's user avatar
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