Related papers: Conjugacy classes of commuting nilpotents

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural…

We present a simple description of moduli spaces of torsion-free D-modules (``D-bundles'') on general smooth complex curves X, generalizing the identification of the space of ideals in the Weyl algebra with Calogero-Moser quiver varieties.…

For $k \in \mathbb{Z}_{>0}$, let $\mathcal{H}^{(k)}_{g,n}$ denote the vector bundle over $\mathfrak{M}_{g,n}$ whose every fiber consists of meromorphic $k$-differentials with poles of order at most $k-1$ on a fixed Riemman surface of genus…

The stable converse soul question (SCSQ) asks whether, given a real vector bundle \(E\) over a compact manifold, some stabilization \(E\times\R^k\) admits a metric with non-negative (sectional) curvature. We extend previous results to show…

A reductive homogeneous space $G/H$ is always diffeomorphic to the normal bundle of an orbit of a maximal compact subgroup of $G$. We prove that if $G/H$ admits compact quotients, then the sphere bundle associated to this normal bundle is…

Let $X_{\mathbb{C}}$ be a smooth real affine variety with compact real points $X_{\mathbb{R}}$. We show that $X_{\mathbb{C}}$ is diffeomorphic to the normal bundle of $X_{\mathbb{R}}$ provided that $X_{\mathbb{C}}$ admits a complete…

In this paper we study $\mathcal M(X)$, the set of diffeomorphism classes of smooth manifolds with the simple homotopy type of $X$, via a map $\Psi$ from $\mathcal M(X)$ into the quotient of $K(X)=[X,BSO]$ by the action of the group of…

Let V be a smooth variety defined over the real numbers. Every algebraic vector bundle on V induces a complex vector bundle on the underlying topological space V(C), and the involution coming from complex conjugation makes it a Real vector…

Let $(\Sigma,\tau)$ denote a Riemann surface of genus $g \geq 2$ equipped with an anti-holomorphic involution $\tau$. In this paper we study the topology of the moduli space $M(r,\xi)^\tau$ of stable Real vector bundles over $(\Sigma,\tau)$…

We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as locally finite $\mathbb{C}$-homs between…

We consider the moduli space MN of flat unitary connections on an open Kaehler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection and L2 cohomologies with…

The natural generalization of the notion of bundle in quantum geometry is that of bimodule. If the base space has quantum group symmetries one is particularly interested in bimodules covariant (equivariant) under these symmetries. Most…

Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \mathrm{Sym}^2(V) \ra \mathcal{O}_X$ (respectively symplectic form $q: \Lambda^2V \ra \mathcal{O}_X$). Fixing the degeneracy locus of the…

This paper develops the tools of formal algebraic geometry in the setting of noncommutative manifolds, roughly ringed spaces locally modeled on the free associative algebra. We define a notion of noncommutative coordinate system, which is a…

Fix $n\geq 5$ general points $p_1, \dots, p_n\in\mathbb{P}^1$, and a weight vector $\mathcal{A} = (a_{1}, \dots, a_{n})$ of real numbers $0 \leq a_{i} \leq 1$. Consider the moduli space $\mathcal{M}_{\mathcal{A}}$ parametrizing rank two…

Let SU_X(n,L) be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g>1 curve X. Let SU_X^s(n,L) denote the open subset parameterizing stable bundles. We show that for small i, the…

Let ${\mathcal M}$ be a moduli space of stable vector bundles of rank $r$ and determinant $\xi$ on a compact Riemann surface $X$. Fix a semistable holomorphic vector bundle $F$ on $X$ such that $\chi(E\otimes F)= 0$ for $E \in \mathcal M$.…

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

Let K be an infinite field and denote by H(n,K) the family of pairs (A,B) of commuting nilpotent n by n matrices with entries in K. There has been substantial recent study of the connection between H(n,K) and the fibre H[n] of the punctual…