In algebraic geometry and

complex geometry In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and c ...

, 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 In mathematics, the general linear group of degree ''n'' is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, ...

; i.e., the moduli stack was the

moduli stack of vector bundles In algebraic geometry, the moduli stack of rank-''n'' vector bundles Vect''n'' is the stack parametrizing vector bundles (or locally free sheaves) of rank ''n'' over some reasonable spaces. It is a smooth algebraic stack of the negative dimension ...

, 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.http://www.math.harvard.edu/~lurie/282ynotes/LectureIII-Cohomology.pdf

References

Further reading