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
[edit]- ^ Behrend 2003
- ^ Lurie, Jacob (February 5, 2014). "Cohomological Formulation (Lecture 3)" (PDF). Harvard University.
- Behrend, Kai A. (2003). The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles (PDF) (PhD). University of British Columbia.
Further reading
[edit]- Nitin Nitsure, Schematic Harder-Narasimhan Stratification
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