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10 - Line Geometry

Published online by Cambridge University Press:  11 August 2026

Igor V. Dolgachev
Igor V. Dolgachev
Affiliation:
University of Michigan, Ann Arbor
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Summary

We study the classical geometry of lines in a projective space. In particular, we discuss the quadratic line complexes and the associated Kummer surfaces. We discuss the geometry of scolls and present the classification of quartic ruled surfaces.

Keywords

Grassmannian varietiesline complexesKummer surfaces

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Type
Chapter
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Classical Algebraic Geometry
A Modern View
 , pp. 192 - 286
Publisher: Cambridge University Press
Print publication year: 2026

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  • Line Geometry
  • Igor V. Dolgachev, University of Michigan, Ann Arbor
  • Book: Classical Algebraic Geometry
  • Online publication: 11 August 2026
  • Chapter DOI: https://doi.org/10.1017/9781009759762.005
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  • Line Geometry
  • Igor V. Dolgachev, University of Michigan, Ann Arbor
  • Book: Classical Algebraic Geometry
  • Online publication: 11 August 2026
  • Chapter DOI: https://doi.org/10.1017/9781009759762.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Line Geometry
  • Igor V. Dolgachev, University of Michigan, Ann Arbor
  • Book: Classical Algebraic Geometry
  • Online publication: 11 August 2026
  • Chapter DOI: https://doi.org/10.1017/9781009759762.005
Available formats
×