International Mathematics Research Notices - current issue

Subscriptions

Fri, 20 Nov 2009 01:19:37 PST

Editors

Fri, 20 Nov 2009 01:19:37 PST

Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames

Lam, C. H., Shimakura, H. — Fri, 20 Nov 2009 01:19:37 PST

In this paper, we study certain Virasoro frames for lattice vertex operator algebras (VOAs) and their -orbifolds using linear codes over . We also compute the corresponding frame stabilizer from the viewpoint of binary codes and -codes. As an application, we determine the frame stabilizers of several Virasoro frames of the VOA and the moonshine vertex operator algebra V.

Symmetric Waves Are Traveling Waves

Ehrnstrom, M., Holden, H., Raynaud, X. — Fri, 20 Nov 2009 01:19:37 PST

We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class of nonlinear partial differential equations, including some of the most famous model equations for water waves. A detailed analysis is given for weak solutions of the Camassa–Holm equation. In addition, we establish the existence of nonsymmetric linear rotational waves for the Euler equations.

Moduli of Bundles over Rational Surfaces and Elliptic Curves II: Nonsimply Laced Cases

Leung, N. C., Zhang, J. — Fri, 20 Nov 2009 01:19:37 PST

For any nonsimply laced Lie group G and elliptic curve , we show that the moduli space of flat G bundles over can be identified with the moduli space of rational surfaces with G-configurations which contain as an anticanonical curve. We also construct Lie(G)-bundles over these surfaces. The corresponding results for simply laced groups were obtained by the authors in another paper. Thus, we have established a natural identification for these two kinds of moduli spaces for any Lie group G.

Rational Curves on Smooth Cubic Hypersurfaces

Coskun, I., Starr, J. — Fri, 20 Nov 2009 01:19:37 PST

We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hypersurface in of degree 2d ≤ min (n + 4, 2n – 2) and dimension at least three is irreducible and of the expected dimension.

Stable String Operations Are Trivial

Tamanoi, H. — Fri, 20 Nov 2009 01:19:37 PST

We show that in closed string topology and in open-closed string topology with one D-brane, higher genus stable string operations are trivial. This is a consequence of Harer's stability theorem and related stability results on the homology of mapping class groups of surfaces with boundaries. In fact, this vanishing result is a special case of a general result that applies to all homological conformal field theories with the property that in the associated topological quantum field theories, the string operations associated to genus 1 cobordisms with one or two boundaries vanish. In closed string topology, the base manifold can be either finite-dimensional, or infinite-dimensional with finite-dimensional cohomology for its based loop space. The above vanishing result is based on the triviality of string operations associated to the homology classes of mapping class groups that are in the image of stabilizing maps.

Holomorphic Line Bundles on Projective Toric Manifolds from Lagrangian Sections of their Mirrors by SYZ Transformations

Chan, K. — Fri, 20 Nov 2009 01:19:37 PST

The mirror of a projective toric manifold is given by a Landau–Ginzburg model (Y, W). We introduce a class of Lagrangian submanifolds in (Y, W) and show that, under the SYZ mirror transformation, they can be transformed to torus-invariant Hermitian metrics on holomorphic line bundles over . Through this geometric correspondence, we also identify the mirrors of Hermitian–Einstein metrics, which are given by distinguished Lagrangian sections whose potentials satisfy certain Laplace-type equations.

Integral Chow Rings of Toric Stacks

Iwanari, I. — Fri, 20 Nov 2009 01:19:37 PST

The goal of this paper is to compute integral Chow rings of toric stacks and prove that they are naturally isomorphic to Stanley–Reisner rings.

The Fate of the Landau Levels under Perturbations of Constant Sign

Klopp, F., Raikov, G. — Fri, 20 Nov 2009 01:19:37 PST

We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrödinger operator with a constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of the perturbed problem.