相关论文: Geometry of equivariant compactifications of $G^n_…

We classify generically transitive actions of semidirect products of an additive and a multiplicative group on the projective plane. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's…

Under Poincar\'e duality, a smooth map of compact oriented manifolds induces a pushforward map in cohomology, called the "Gysin map." It plays an important role in enumerative geometry. Using the equivariant localization formula, the author…

We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…

In this paper, the authors apply a stratification of moduli spaces of complex Lie algebras to analyzing the moduli spaces of nxn matrices under scalar similarity and bilinear forms under the cogredient action. For similar matrices, we give…

We define and study an equivariant version of Farber's topological complexity for spaces with a given compact group action. This is a special case of the equivariant sectional category of an equivariant map, also defined in this paper. The…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

We describe the $G$-equivariant Grothendieck ring of a regular compactification $X$ of an adjoint symmetric space $G/H$ of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

In this paper, we study all ways of constructing modular compactifications of the moduli space $\mathcal{M}_{g,n}$ of $n$-pointed smooth algebraic curves of genus $g$ by allowing markings to collide. We find that for any such…

We define and discuss G-formality for certain spaces endowed with an action by a compact Lie group. This concept is essentially formality of the Borel construction of the space in a category of commutative differential graded algebras over…

As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows…

A connection between moduli spaces of algebro-geometric objects and moduli spaces of polyhedral objects has been under investigation in recent years. Loosely speaking, the skeleton of an algebro-geometric moduli space is expressed as the…

In a previous paper we have constructed a compactification $KGl_n$ of the general linear group $Gl_n$, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De…

Let $\mathrm G$ be an isotrivial reductive group over a scheme $S$. We construct a smooth projective $S$-scheme containing $\mathrm G$ as a fiberwise-dense open subscheme equipped with left and right actions of $\mathrm G$ which extend the…

For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduce to the moduli space of stable curves and a…

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary…

We survey two new compactification methods for the KSBA moduli space of general type surfaces so that both of them admit a perfect obstruction theory. Virtual fundamental classes exist on these two moduli spaces, and tautological invariants…

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 associated quotient variety. In this article we describe how…

In this article, we investigate the category $\mathcal{A}^G$ of equivariant objects of an additive category $\mathcal{A}$ with respect to an action of a finite group $G$. We show that if $G$ is solvable then we can reconstruct $\mathcal{A}$…

Let $G$ be a simple complex algebraic group, $P$ a parabolic subgroup of $G$ and $N$ the unipotent radical of $P.$ The so-called equivariant compactification of $N$ by $G/P$ is given by an action of $N$ on $G/P$ with a dense open orbit…