Setayesh, Iman

Let $D$ be a smooth divisor on a non singular surface $S$. We compute Betti numbers of the relative Hilbert scheme of points of $S$ relative to $D$. In the case of $\PP^2$ and a line in it, we give an explicit set of generators and relations for the cohomology groups of this space.

Kichenassamy, Satyanad Rendall, Alan D.

We use Fuchsian Reduction to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized, or other known solutions. The method provides precise asymptotics at the singularity, which is Kasner-like. All of these...

Kichenassamy, Satyanad

This paper presents an asymptotic reduction of the Einstein-Klein-Gordon system with real scalar field ("soliton star problem"). A periodic solution of the reduced system, similar to the sine-Gordon breather, is obtained by a variational method. This tallies with numerical computations. As a consequence, a time-periodic redshift for sources close t...

Feingold, Alex J. Kleinschmidt, Axel Nicolai, Hermann

We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of the division algebras and associated discrete matrix groups. Our findings can be summarized by saying...

Pandharipande, R. Thomas, R. P.

We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and Behrend's constructible function approach to the virtual class. We prove that for irreducible classes the stable pairs generating function satisfies the strong BPS r...

Fujii, Shigeyuki Minabe, Satoshi

This is an expository paper which has two parts. In the first part, we study quiver varieties of affine $A$-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating function of Poincare polynomials of quiver varieties in rank 1 cases. Our main tools are cores and quotients of Young...

Clarke, Patrick

We introduce a duality construction for toric Landau–Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau–Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, Berglund–Hübsch, Givental, and Hori–Vafa. It can be done in more general situations, and provide...

Alho, Artur Valiente Kroon, Juan A. Mena, Filipe C.

A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the Einstein–Euler system. The resulting evolution system is used to show that small nonlinear perturbations of ex...

Bergshoeff, E. Chemissany, W. Ploegh, A. Trigiante, M. Van Riet, T.

We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike $p$-brane solutions when they are lifted over a $p$-dimensional flat space. In particular, we consider the problem of constructing \emph{the minimal g...

Kawabata, Kiyoshi Limaye, Sanjay S.

We first establish a simple procedure to obtain with 11-figure accuracy the values of Chandrasekhar's H-function for isotropic scattering using a closed-form integral representation and the Gauss-Legendre quadrature. Based on the numerical values of the function produced by this method for various values of the single scattering albedo and the cosi...