The finite unipotent groups consisting of bireflections

Let k be a field of characteristic p and V a finite-dimensional k-vector space. An element {g\in{\rm GL}(V)} is called a bireflection if it centralizes a subspace of codimension less than or equal to 2. It is known by a result of Kemper that if for a finite p-group {G\leq{\rm GL}(V)} the ring of invariants {{\rm Sym}(V^{*})^{G}} is Cohen–Macaulay, G is generated by bireflections. Although the converse is false in general, it holds in special cases e.g. for particular families of groups consisting of bireflections. In this paper we give, for {p>2} , a classification of all finite unipotent subgroups of {{\rm GL}(V)} consisting of bireflections. Our description of the groups is given explicitly in terms useful for exploring the corresponding rings of invariants. This further analysis will be the topic of a forthcoming paper.

Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable K\"ahler structures obtained by symplectic reduction. The relation of our complex-analytic theory to the work of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group actions on projective varieties is discussed in detail. Comment: v2: 30 pages, final version as accepted by EPIGA