nLab
geometric invariant theory

Idea

Geometric invariant theory studies the construction of moduli spaces / moduli stacks in terms of quotients / action groupoids.

This is the geometric aspect (Isbell dual aspect) of invariant theory.

Related concepts

• stability, stable vector bundle

References

• David Mumford, John Fogarty, Frances Clare Kirwan, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) 34, Springer-Verlag

• David Mumford, Stability of projective varieties, L’Enseignement Mathématique 23 (1977) doi

• David J. Swinarski, Geometric Invariant Theory and Moduli Spaces of Maps (pdf)

• Jürgen Hausen, A generalization of Mumford’s geometric invariant theory (pdf)