Logarithmic geometry, minimal free resolutions and toric algebraic stacks

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13 Citations (Scopus)


In this paper we will introduce a certain type of morphisms of log schemes (in the sense of Fontaine, Illusie and Kato) and study their moduli. Then by applying this we define the notion of toric algebraic stacks, which may be regarded as torus emebeddings in the framework of algebraic stacks and prove some fundamental properties. Also, we study the stack-theoretic analogue of toroidal embeddings.

Original languageEnglish
Pages (from-to)1095-1140
Number of pages46
JournalPublications of the Research Institute for Mathematical Sciences
Issue number4
Publication statusPublished - 2009 Dec


  • Algebraic stacks
  • Logarithmic geometry
  • Toric geometry


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