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The Multidegree of the Multi-Image Variety

  • Laura EscobarEmail author
  • Allen Knutson
Chapter
Part of the Fields Institute Communications book series (FIC, volume 80)

Abstract

The multi-image variety is a subvariety of \(\mathop{\mathrm{Gr}}\nolimits (1, \mathbb{P}^{3})^{n}\) that parametrizes all of the possible images that can be taken by n fixed cameras. We compute its cohomology class in the cohomology ring of \(\mathop{\mathrm{Gr}}\nolimits (1, \mathbb{P}^{3})^{n}\) and its multidegree as a subvariety of \((\mathbb{P}^{5})^{n}\) under the Plücker embedding.

MSC 2010 codes:

14M15,14Nxx 

Notes

Acknowledgements

This article was initiated during the Apprenticeship Weeks (22 August–2 September 2016), led by Bernd Sturmfels, as part of the Combinatorial Algebraic Geometry Semester at the Fields Institute for Research in Mathematical Sciences. The authors would like to thank their anonymous referees as well as Jenna Rajchgot and Bernd Sturmfels. The first author was supported by the Fields Institute for Research in Mathematical Sciences.

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Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

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