167 citations · 315 across the 18 of their papers we have counts for
19 papers
Graded linearisations
Gergely Bérczi, Brent Doran, Frances Kirwan
When the action of a reductive group on a projective variety has a suitable linearisation, Mumford's geometric invariant theory (GIT) can be used to construct and study an associat…
Projective completions of graded unipotent quotients
Gergely Bérczi, Brent Doran, Thomas Hawes +1
The aim of this paper is to show that classical geometric invariant theory (GIT) has an effective analogue for linear actions of a non-reductive algebraic group with graded uni…
Geometric invariant theory for graded unipotent groups and applications
Gergely Bérczi, Brent Doran, Thomas Hawes +1
Let be a graded unipotent group over the complex numbers, in the sense that it has an extension by the multiplicative group such that the action of the multiplicative…
Algebraic symplectic analogues of additive quotients
Brent Doran, Victoria Hoskins
Motivated by the study of hyperkahler structures in moduli problems and hyperkahler implosion, we initiate the study of non-reductive hyperkahler and algebraic symplectic quotients…
Constructing quotients of algebraic varieties by linear algebraic group actions
Gergely Bérczi, Brent Doran, Thomas Hawes +1
In this article we review the question of constructing geometric quotients of actions of linear algebraic groups on irreducible varieties over algebraically closed fields of charac…
Symplectic and hyperkahler implosion
Andrew Dancer, Brent Doran, Frances Kirwan +1
We review the quiver descriptions of symplectic and hyperkähler implosion in the case of SU(n) actions. We give quiver descriptions of symplectic implosion for other classical grou…