Harder–Narasimhan stratification

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

1. ↑ Behrend 2003
2. ↑ 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). University of British Columbia.

## Further reading

* Nitin Nitsure, Schematic Harder-Narasimhan Stratification

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