Harder–Narasimhan stratification
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In algebraic geometry and complex geometry, the Harder–Narasimhan stratification is any of a stratification of the moduli stack of principal G-bundles by locally closed substacks in terms of "loci of instabilities". In the original form due to Harder and Narasimhan, G was the general linear group; i.e., the moduli stack was the moduli stack of vector bundles, but, today, the term refers to any of generalizations. The scheme-theoretic version is due to Shatz and so the term "Shatz stratification" is also used synonymously. The general case is due to Behrend.[1][2]
References
- ↑ Behrend (2003).
- ↑ Lurie, Jacob (February 5, 2014). "Cohomological Formulation (Lecture 3)". Harvard University. http://www.math.harvard.edu/~lurie/282ynotes/LectureIII-Cohomology.pdf.
- Behrend, Kai A. (2003). The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles (PDF) (PhD thesis). University of British Columbia. Archived (PDF) from the original on 25 August 2026. Retrieved 24 August 2026.
Further reading
- Nitin Nitsure, Schematic Harder-Narasimhan Stratification
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