20 citations · 154 across the 33 of their papers we have counts for
25 papers · 1 filter
Moment maps and cohomology of non-reductive quotients
Gergely Bérczi, Frances Kirwan
Let be a complex linear algebraic group with internally graded unipotent radical acting on a complex projective variety . Given an ample linearisation of the action and an a…
Non-reductive geometric invariant theory and hyperbolicity
Gergely Bérczi, Frances Kirwan
The Green--Griffiths--Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric i…
Symplectic quotients of unstable Morse strata for normsquares of moment maps
Frances Kirwan
Let K be a compact Lie group and fix an invariant inner product on its Lie algebra. Given a Hamiltonian action of K on a compact symplectic manifold X, the normsquare of the moment…
Variation of Non-reductive Geometric Invariant Theory
Gergely Bérczi, Joshua Jackson, Frances Kirwan
The wall-and-chamber structure of the dependence of the reductive GIT quotient on the choice of linearisation is well known. In this article, we first give a brief survey of recent…
Stratifying quotient stacks and moduli stacks
Gergely Bérczi, Victoria Hoskins, Frances Kirwan
Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective…
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…