Related papers: Equivariant geometry of low-dimensional quadrics
We study linear actions of finite groups in small dimensions, up to equivariant birationality.
We study linearizability of actions of finite groups on cubic threefolds with non-isolated singularities.
We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.
We study linearizability of actions of finite groups on cubic threefolds with nonnodal isolated singularities.
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
We study linearizability and stable linearizability of actions of finite groups on the Segre cubic and Burkhardt quartic, using techniques from group cohomology, birational rigidity, and the Burnside formalism.
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…
We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of…
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…
For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant…
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of…
We study equivariant unirationality of actions of finite groups on tori of small dimensions.
We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse…
We prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly. This solves a…
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…
Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…
We prove uniqueness of equivariant harmonic maps into irreducible symmetric spaces of non-compact type and Euclidean buildings associated to isometric actions by Zariski dense subgroups.