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I - The Geometry of Monoids

Published online by Cambridge University Press:  02 November 2018

Arthur Ogus
Arthur Ogus
Affiliation:
University of California, Berkeley
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Summary

Chapter Istudies the category of commutative integral monoids, especiallyso-called “fine monoids”which are the basic building blocks of toric and logarithmic geometry.It includes a self-contained treatment of standard results in convex geometry, including finiteness and duality and the geometry of faces and ideals, and also discusses the affine toric varieties arising from monoid algebras.In addition to these classical results, it includes a study of limits and colimits of monoids, of actions of monoids on sets,and ofhomomorphisms of monoids, including the key concepts of exact, integral, and saturated homomorphisms.

Keywords

limits of monoidsmonoid actionsmonoid homomorphismsideals and facesduality for monoidsconesaffine toric varietiesexact homomorphismsintegral homomorphismssaturated homomorphisms
Type
Chapter
Information
Lectures on Logarithmic Algebraic Geometry , pp. 1 - 183
Publisher: Cambridge University Press
Print publication year: 2018

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  • The Geometry of Monoids
  • Arthur Ogus, University of California, Berkeley
  • Book: Lectures on Logarithmic Algebraic Geometry
  • Online publication: 02 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781316941614.002
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  • The Geometry of Monoids
  • Arthur Ogus, University of California, Berkeley
  • Book: Lectures on Logarithmic Algebraic Geometry
  • Online publication: 02 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781316941614.002
Available formats
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  • The Geometry of Monoids
  • Arthur Ogus, University of California, Berkeley
  • Book: Lectures on Logarithmic Algebraic Geometry
  • Online publication: 02 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781316941614.002
Available formats
×