Related papers: Convexity theorems for varieties invariant under a…

The main result of this paper is a quasi-hamiltonian analogue of a special case of the O'Shea-Sjamaar convexity theorem for usual momentum maps. We denote by U a simply connected compact connected Lie group and we fix an involutive…

In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode…

Let $X$ be a proper algebraic scheme over an algebraically closed field. We assume that a torus $T$ acts on $X$ such that the action has isolated fixed points. The $T$-graph of $X$ can be defined using the fixed points and the one…

In this note we prove a more general (and topological) version of Gr\"unbaum's conjecture about affine invariant points. As an application of our result we show that, if we consider the action of the group of similarities, Gr\"unbaum's…

Let $X$ be a complex scheme acted on by an affine algebraic group $G$. We prove that the Atiyah class of a $G$-equivariant perfect complex on $X$, as constructed by Huybrechts and Thomas, is $G$-equivariant in a precise sense. As an…

In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…

For some $g \geq 3$, let $\Gamma$ be a finite index subgroup of the mapping class group of a genus $g$ surface (possibly with boundary components and punctures). An old conjecture of Ivanov says that the abelianization of $\Gamma$ should be…

We show that the torsion in the group of indecomposable $(2,1)$-cycles on a smooth projective variety over an algebraically closed field is isomorphic to a twist of its Brauer group, away from the characteristic. In particular, this group…

We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient…

In a recent joint work with V. Turaev (cf. math.DG/9810114) we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemeister torsion it has the advantage of having a well-defined…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

We relate the Brauer group of a smooth variety over a p-adic field to the geometry of the special fibre of a regular model, using the purity theorem in \'etale cohomology. As an illustration, we describe how the Brauer group of a smooth del…

We introduce a new method for proving twisted homological stability, and use it to prove such results for symmetric groups and general linear groups. In addition to sometimes slightly improving the stable range given by the traditional…

In this note we investigate the idea of Michael Atiyah of using, as a possible approach to the Theorem of Feit-Thompson on the solvability of finite groups of odd order, the iterations of the transformation which replaces a representation…

Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a…

In [I. Arzhantsev and M. Zaidenberg, Acyclic curves and group actions on affine toric surfaces. Affine Algebraic Geometry, 1--41. World Scientific Publishing Co. 2013] we described the automorphism groups of the cyclic quotients of the…

We develop several combinatorial models that are useful in the study of the $SL_n$-variety $\mathcal{X}$ of complete quadrics. Barred permutations parameterize the fixed points of the action of a maximal torus $T$ of $SL_n$, while…

Using the Atiyah class we give a criterion for a vector bundle on a coisotropic subvariety, $Y$, of an algebraic Poisson variety $X$ to admit a first and second order noncommutative deformation. We also show noncommutative deformations of a…

In the mid 1980s, while working on establishing completion theorems for equivariant Algebraic K- Theory similar to the well-known Atiyah-Segal completion theorem for equivariant topological K-theory, the late Robert Thomason found the…

We generalize the completion theorem for equivariant MU-module spectra for finite groups or finite extensions of a torus to compact Lie groups using the splitting of global functors proved by Schwede. This proves a conjecture of Greenlees…