A Fano variety is a projective variety whose anticanonical class is ample. A 2–dimensional Fano variety is called a Del Pezzo surface. In higher dimensions, attention originally centered on smooth Fano 3–folds, but singular Fano varieties are also of considerable interest in connection with the minimal model program. The existence of Kähler–Einstein metrics on Fano varieties has also been explo...

A multimodal method based on the admittance matrix is used to analyze wave propagation through scatterers of arbitrary shape. Two cases are considered: a waveguide containing scatterers, and the scattering of a plane wave at oblique incidence to an infinite periodic row of scatterers. In both cases, the problem reduces to a system of two sets of first-order differential equations for the modal ...

We complete the study of birational geometry of Fano fiber spaces π: V → P 1 , the fiber of which is a Fano double hypersurface of index 1. For each family of these varieties we either prove birational rigidity or produce explicitly non-trivial structures of Fano fiber spaces. A new linear method of studying movable systems on Fano fiber spaces V /P 1 is developed. Bibliography: 17 titles.

We propose a simple structure of a silver nanorice heterodimer to achieve both Fano resonances and strong optical activity. Due to the ellipsoid shape of nanorice, the dimer shows a unique plasmon hybridization picture, being different from those in previously studied two-nanoparticle coupling, which benefits the generation of Fano resonances here. Under oblique incidence, this nanorice dimer e...

Introduction In the 1970s, Reid introduced the graded rings method for the explicit classification of surfaces, which he used to produce a list of 95 K3 quasi-smooth hypersurfaces in weighted projective spaces (which were proved to be the only ones). Later, Fletcher used this method to create more lists of different weighted complete intersections. From the K3 surfaces he developed two lists of...

Submitted for the MAR08 Meeting of The American Physical Society Fano-Kondo effect in a two-level system with triple quantum dots TETSUFUMI TANAMOTO, YOSHIFUMI NISHI, SHINOBU FUJITA, Advanced LSI Technology Laboratory, Toshiba Corporation — Quantum dot (QD) systems have been providing opportunities to probe a wide variety of many-body effects in microelectronic structures. Recently, the Fano ef...

Mikhail V. Rybin,1,2,* Polina V. Kapitanova,2 Dmitry S. Filonov,2 Alexey P. Slobozhanyuk,2 Pavel A. Belov,2 Yuri S. Kivshar,2,3 and Mikhail F. Limonov1,2 1Ioffe Physical-Technical Institute, St. Petersburg 194021, Russia 2National Research University for Information Technology, Mechanics and Optics (ITMO), St. Petersburg 197101, Russia 3Nonlinear Physics Center, Research School of Physics and E...

In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We show that any centrally symmetric or pseudosymmetric smooth Fano polytopes can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of smooth Fano polytopes whose corresponding...

In [Ru2] we have classified the smooth projective symmetric G-varieties with Picard number one (and G semisimple). In this work we give a geometrical description of such varieties. In particular, we determine their group of automorphisms. When this group, Aut(X), acts non-transitively on X, we describe a G-equivariant embedding of the variety X in a homogeneous variety (with respect to a larger...

This paper presents an experimental demonstration of pronounced Fano resonances in a remarkably simple, three-dimensional (3D) plasmonic system, composed of two groups of paired cut-wires with different sizes. Theoretical calculations using the Finite Element Method, which are in good agreement with the experiment, are provided to describe the Fano behaviour. The dependence of the Fano line sha...