Related papers: The exterior splash in PG(6,q): Transversals

Let $\pi$ be a non-self-dual unitary cuspidal automorphic representation of non-solvable polyhedral type for GL(2) over a number field. We show that $\pi$ has a positive upper Dirichlet density of Hecke eigenvalues in any sector whose angle…

Let S be a closed, connected, orientable surface of genus at least 2, and let C(S) denote the deformation space of convex real projective structures S. In this article, we introduce two new flows on C(S), which we call the internal bulging…

We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…

To each non-isotropic almost-complex immersion of a 2-torus into $ S ^ 6 $ we associate an algebraic curve, called the spectral curve, and a linear flow in the intersection of two Prym varieties on this spectral curve. We show that…

For $q = p^n$ with $p$ an odd prime, the projective linear group $PGL(2,q)$ can be seen as the stabilizer of a conic $O$ in a projective plane $\pi = PG(2,q)$. In that setting, involutions of $PGL(2,q)$ correspond bijectively to points of…

The point-pushing subgroup P(S) of the mapping class group Mod(S) of a surface with marked point is an embedding of \pi_1(S) given by pushing the marked point around loops. We prove that for g>=3, the subgroup P(S) is the unique normal,…

The inability of standard models to explain the flux ratios in many 4-image gravitational lenses has been cited as evidence for significant small-scale structure in lens galaxies. That claim has generally relied on detailed lens modeling,…

Given a cuspidal automorphic representation $\pi$ for GL(3) over a number field and a positive integer $k$, assume that the symmetric $m$th power lifts of $\pi$ are isobaric automorphic for $m \leq k$, cuspidal for $m \leq k-1$, and that…

We construct the first known example of a near horizon supergravity solution for a pair of NS5-branes, intersecting on R^{1,3} and localised in all directions except a single transverse circle. We do this by establishing an explicit map…

This is a summary of the work in the author's recent paper with this title written with Jerome Gauntlett, George Papadopoulos and Paul Townsend, hep-th/9702202. We showed how to construct hyper-K\"ahler 8-metrics in terms of arrangements of…

We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…

$\xi$-submanifold in the Euclidean space $\bbr^{m+p}$ is a natural extension of the concept of self-shrinker to the mean curvature flow in $\bbr^{m+p}$. It is also a generalization of the $\lambda$-hypersurface defined by Q.-M. Cheng et al…

Let $ \CO $ be the ring of integers of a non-Archimedean local field and $ \pi $ a fixed uniformizer of $ \CO $. We establish three main results. The first one states that the exterior powers of a $ \pi $-divisible $ \CO $-module scheme of…

This is an investigation into a classification of embeddings of a surface in Euclidean $3$-space. Specifically, we consider $\mathbb{R}^3$ as having the product structure $\mathbb{R}^2 \times \mathbb{R}$ and let $\pi:\mathbb{R}^2 \times…

Recent HI observations reveal that the discs of spiral galaxies are surrounded by extended gaseous haloes. This extra-planar gas reaches large distances (several kpc) from the disc and shows peculiar kinematics (low rotation and inflow). We…

The present work constitutes the third installment in a series of investigations devoted to discrete conformal structures on surfaces with boundary. In our preceding works \cite{X-Z DCS1, X-Z DCS2}, we established, respectively, a…

We present HI synthesis maps of the edge-on starburst NGC 5433 and its environment, obtained with the VLA in its C and D configurations. The observations and spectral model residuals of the main disc emission in NGC 5433 reveal 3…

We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our…

An affine spread is a set of subspaces of $\mathrm{AG}(n, q)$ of the same dimension that partitions the points of $\mathrm{AG}(n, q)$. Equivalently, an {\em affine spread} is a set of projective subspaces of $\mathrm{PG}(n, q)$ of the same…

This paper deals with complex structures on Lie algebras $\ct_{\pi} \hh=\hh \ltimes_{\pi} V$, where $\pi$ is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on $\ct_{\pi}…