Related papers: A Hasse diagram for rational toral ranks

Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…

Let X be a smooth projective toric surface, and H^d(X) the Hilbert scheme parametrising the length d zero-dimensional subschemes of X. We compute the rational Chow ring A^*(H^d(X))\_Q. More precisely, if T is the two-dimensional torus…

For each finite ordinal n, and each locally-finite group G of cardinality aleph-sub-n, we construct an (n+1)-dimensional, contractible CW-complex on which G acts with finite stabilizers. We use the complex to obtain information about…

Let $P=G/K$ be a semisimple non-compact Riemannian symmetric space, where $G=I_0(P)$ and $K=G_p$ is the stabilizer of $p\in P$. Let $X$ be an orbit of the (isotropy) representation of $K$ on $T_p(P)$ ($X$ is called a real flag manifold).…

Suppose that an algebraic torus $G$ acts algebraically on a projective manifold $X$ with generically trivial stabilizers. Then the Zariski closure of the set of pairs $\{(x,y)\in X\times X\mid y=gx \text{for some}g\in G\}$ defines a nonzero…

For a semisimple complex algebraic group $G$ we determine the rational cohomology and the Hodge-Tate structure of the moduli stack ${\mathscr B}un_{G,X}$ of principal $G$-bundles over a connected smooth complex projective variety $X$ of…

We study normal compact K\"ahler spaces whose rational cohomology ring is isomorphic to that of a complex torus. We call them rational cohomology tori. We classify, up to dimension three, those with rational singularities. We then give…

Let $\FN$ be a free group of finite rank $N \geq 2$, and let $T$ be an $\R$-tree with a very small, minimal action of $\FN$ with dense orbits. For any basis $\CA$ of $\FN$ there exists a {\em heart} $K_{\CA} \subset \bar T$ (= the metric…

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…

We show that the property of being rationally $K$-stable passes from the fibers of a continuous $C(X)$-algebra to the ambient algebra, under the assumption that the underlying space $X$ is compact, metrizable, and of finite covering…

We classify all rational maps $H \in K(x)^n$ for which ${\rm trdeg}_K K(tH_1,tH_2,\ldots,tH_n) \le 2$, where $K$ is any field and $t$ is another indeterminate. Furthermore, we classify all such maps for which additionally $JH \cdot H = {\rm…

Let $G$ be an infinite discrete group. A classifying space for proper actions of $G$ is a proper $G$-CW-complex $X$ such that the fixed point sets $X^H$ are contractible for all finite subgroups $H$ of $G$. In this paper we consider the…

For any simplicial complex $X$ with a total ordering of its vertices, one can construct a chain complex $\mathbb{L}_\bullet(X)$ generated by necklaces of simplices in $X$, which computes the homology of the free loop space of the geometric…

For any crystallographic root system, let $W$ be the associated Weyl group, and let $\mathit{WP}$ be the weight polytope (also known as the $W$-permutohedron) associated with an arbitrary strongly dominant weight. The action of $W$ on…

Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert…

We prove several basic ring-theoretic results about tautological rings of manifolds W, that is, the rings of generalised Miller--Morita--Mumford classes for fibre bundles with fibre W. Firstly we provide conditions on the rational…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

Hjorth has introduced a Scott analysis for general Polish group actions, and has asked whether his notion of rank satisfies a boundedness principle similar to the one of Scott rank - namely, the orbit equivalence relation is Borel if and…

Let X be a Mori dream space together with an effective torus action of complexity one. In this note, we construct a polyhedral divisor on a suitable covering of the projective line P^1 which corresponds to the affine spectrum of the Cox…

We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and…