Quotients: Geometrical Properties

This lecture explores the geometrical properties of quotients by linearly reductive groups, focusing on the surjectivity and submersiveness of the quotient map, the uniqueness of closed orbits in each fiber, and the concept of a geometric quotient when all orbits are closed. The lecture also discusses how the quotient map defines equivalence relations based on the closure of orbits, emphasizing the importance of closed orbits in determining the structure of the quotient space.