A Nakajima quiver variety is a symplectic quotient constructed from the cotangent space of a framed quiver representation
space with a stability condition. For a finite quiver 
and complex spaces 
, put
 |
For the cotangent moment map 
and a character 
of 
, the stable quotient is 
. When semistability equals stability
and 
acts freely on that locus, the quotient is smooth. Such a stability character is
called regular here, and the stable locus is allowed to be empty.
Loops and multiple arrows are permitted. A torus acting on 
and commuting with 
gives equivariant parameters. The cohomology
algebra of the quotient is compared with a fixed subscheme of the associated Coulomb
branch in the Hikita conjecture.
