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Appendix B - Local Positivity of Intersections

Published online by Cambridge University Press:  06 March 2020

Chris Wendl
Affiliation:
Humboldt-Universität zu Berlin
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Summary

The primary goal of this appendix is to explain a more or less self-contained proof of local positivity of intersections for holomorphic curves. The exposition begins with a survey of the main results needed from elliptic regularity theory; here most of the proofs are only sketched, but an effort is made to include all of the important ideas and avoid unnecessary technical overhead (e.g., we do not need to use the Calderon–Zygmund inequality). This leads to a proof of the similarity principle, and the latter is the main tool needed for proving a local representation formula that may be viewed as a “weak version” of the Micallef–White theorem. This representation formula is then used to prove positivity of intersections and give a precise definition of the local singularity index for a nonconstant holomorphic curve in dimension 4.

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Publisher: Cambridge University Press
Print publication year: 2020

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  • Local Positivity of Intersections
  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
  • Online publication: 06 March 2020
  • Chapter DOI: https://doi.org/10.1017/9781108608954.009
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  • Local Positivity of Intersections
  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
  • Online publication: 06 March 2020
  • Chapter DOI: https://doi.org/10.1017/9781108608954.009
Available formats
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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.

  • Local Positivity of Intersections
  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
  • Online publication: 06 March 2020
  • Chapter DOI: https://doi.org/10.1017/9781108608954.009
Available formats
×