15 citations · 53 across the 13 of their papers we have counts for
18 papers
Chow polynomials and chain polynomials of matroids are not log-concave
Gergely Bérczi, Basile Coron, Christopher Eur +1
The Hilbert--Poincaré series of the Chow rings of the toric varieties of matroids, often called the \emph{Chow polynomials}, and the -polynomial of their boundary complexes, cal…
Stratified motivic invariants and bivariate deformations of Poincaré polynomials
Gergely Bérczi, Young-Hoon Kiem
For a stratified variety and a motivic invariant , we consider the stratified invariant which interpolates the invariant of and that of its interior …
Real-rootedness of the Poincaré polynomials of : an AI-assisted proof
Gergely Bérczi, Young-Hoon Kiem
We prove real-rootedness for the Poincaré polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\ove…
Multiple-point residue formulas for holomorphic maps
Gergely Bérczi, András Szenes
We develop a new approach to the study of the multipoint loci of holomorphic maps between complex manifolds. We relate the -fold locus to the curvilinear component of the Hilber…
Non-reductive geometric invariant theory and Thom polynomials
Gergely Bérczi
We combine recently developed intersection theory for non-reductive geometric invariant theoretic quotients with equivariant localisation to prove a formula for Thom polynomials of…
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…
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…
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…
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…
Graded unipotent groups and Grosshans theory
Gergely Bérczi, Frances Kirwan
Let be a unipotent group which is graded in the sense that it has an extension by the multiplicative group of the complex numbers such that all the weights of the adjoint a…
Tautological integrals on curvilinear Hilbert schemes
Gergely Bérczi
We take a new look at the curvilinear Hilbert scheme of points on a smooth projective variety as a projective completion of the non-reductive quotient of holomorphic map germs…
Moduli of map germs, Thom polynomials and the Green-Griffiths conjecture
Gergely Bérczi
This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into comple…
Invariants for non-reductive group actions
Gergely Bérczi, Frances Kirwan
We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric con…
On the Popov-Pommerening conjecture for linear algebraic groups
Gergely Bérczi
Let be a reductive group over an algebraically closed subfield of of characteristic zero, an observable subgroup normalized by a maximal torus…