The theory of regular log scheme, roughly specking is that scheme theory with singularities like those of toric varieties.
Dose anyone could explain this idea in detail or give a reference about the relations between log schemes and toric varieties?
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The source text Kato, Kazuya Logarithmic structures of Fontaine-Illusie. Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), 191–224, Johns Hopkins Univ. Press, Baltimore, MD, 1989. available here http://www.math.brown.edu/~abrmovic/LOGGEOM/Kato-log.pdf. Example (3.7) (1) the bottom line is "... essentially, the theory of toroidal embeddings is nothing but the theory of schemes with smooth fine log. str.'s over a field (with respect to the trivial log. str. on the base field)." |
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