Defect and Hodge numbers of hypersurfaces

We define defect for hypersurfaces with A-D-E singularities in complex projective normal Cohen-Macaulay fourfolds having some vanishing properties of Bott-type and prove formulae for Hodge numbers of big resolutions of such hypersurfaces. We compute Hodge numbers of Calabi-Yau manifolds obtained as small resolutions of cuspidal triple sextics and double octics with higher A_j singularities.Comment: 25 page

Quartic double solids with ordinary singularities

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7

Elliptic curve configurations on Fano surfaces

The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That means that we give the number of such curves, their intersections and a plane model. This classification is linked to the classification of the automorphism groups of theses surfaces.Comment: 17 pages, accepted and shortened version, the rest will appear in "Fano surfaces with 12 or 30 elliptic curves

D-brane superpotentials and RG flows on the quintic

The behaviour of D2-branes on the quintic under complex structure deformations is analysed by combining Landau-Ginzburg techniques with methods from conformal field theory. It is shown that the boundary renormalisation group flow induced by the bulk deformations is realised as a gradient flow of the effective space time superpotential which is calculated explicitly to all orders in the boundary coupling constant.Comment: 24 pages, 1 figure, v2:Typo in (3.14) correcte

Brown Dwarfs and the Cataclysmic Variable Period Minimum

Using improved, up-to-date stellar input physics tested against observations of low-mass stars and brown dwarfs we calculate the secular evolution of low-mass donor cataclysmic variables (CVs), including those which form with a brown dwarf donor. Our models confirm the mismatch between the calculated minimum period (Pmin ~ 70 min) and the observed short-period cut-off (~ 80 min) in the CV period histogram. We find that tidal and rotational corrections applied to the one-dimensional stellar structure equations have no significant effect on the period minimum. Theoretical period distributions synthesized from our model sequences always show an accumulation of systems at the minimum period, a feature absent from the observed distribution. We suggest that non-magnetic CVs become unobservable as they are effectively trapped in permanent quiescence before they reach Pmin, and that small-number statistics may hide the period spike for magnetic CVs.Comment: 10 pages; accepted for publication in MNRA

Non-birational twisted derived equivalences in abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kahler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kahler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov's `homological projective duality.' Along the way, we shall see how `noncommutative spaces' (in Kontsevich's sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.Comment: 54 pages, LaTeX; v2: typo fixe

Validity of the Independent-Particle Approximation in X-Ray Photoemission: The Exception, Not the Rule

A combined experimental and theoretical study of argon valence photoionization illustrates the discovery of the broad lack of validity of the independent-particle approximation (IPA) for x-ray photoemission. In addition to previously known breakdowns of the IPA, which are limited to high photon energies and regions very near threshold, the observed breakdown in photoionization at intermediate energies demonstrates generally that the IPA is valid only in very restricted domains. These restrictions are expected to be relevant throughout the periodic table, with consequences for a wide variety of applications

High flux cold Rubidium atomic beam for strongly coupled Cavity QED

This paper presents a setup capable of producing a high-flux continuous beam of cold rubidium atoms for cavity QED experiments in the regime of strong coupling. A 2 $D^+$ MOT, loaded by rubidium getters in a dry film coated vapor cell, fed a secondary moving-molasses MOT (MM-MOT) at a rate of 1.5 x $10^{10}$ atoms/sec. The MM-MOT provided a continuous beam with tunable velocity. This beam was then directed through the waist of a 280 $\mu$m cavity resulting in a Rabi splitting of more than +/- 10 MHz. The presence of sufficient number of atoms in the cavity mode also enabled splitting in the polarization perpendicular to the input. The cavity was in the strong coupling regime, with parameters (g, $\kappa$, $\gamma$)/2$\pi$ equal to (7, 3, 6)/ 2$\pi$ MHz.Comment: Journal pape