In this note we prove the following result. A fine log scheme over the complex numbers and its saturated have homeomorphic Kato-Nakayama associated spaces. Moreover these spaces are isomorphic as ringed spaces, either with the ring sheaf defined by Kato-Nakayama, either with the one defined by Ogus. In the definition of these spaces, non-integral monoids are involved, so that the proof of the result is based on properties of non necessarily integral monoids.
A note on Kato-Nakayama spaces
CAILOTTO, MAURIZIO
2004
Abstract
In this note we prove the following result. A fine log scheme over the complex numbers and its saturated have homeomorphic Kato-Nakayama associated spaces. Moreover these spaces are isomorphic as ringed spaces, either with the ring sheaf defined by Kato-Nakayama, either with the one defined by Ogus. In the definition of these spaces, non-integral monoids are involved, so that the proof of the result is based on properties of non necessarily integral monoids.
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