Abstract:

Algebraic varieties arising from algebraic Hamiltonian reduction are typically singular. However, they frequently admit "nice" resolutions by smooth symplectic varieties. Such resolutions have played a starring role in recent developments in symplectic algebraic geometry. On the other hand, quantizations of the singular varieties lead to beautiful objects of noncommutative algebra, for example, certain rational Cherednik algebras and "hypertoric enveloping algebras." I will explain some special equivalences of derived categories between quantizations of the singular and smooth symplectic varieties and how they generalize classical results in the area. This is joint work with K. McGerty.