In this paper, we classify smooth toric Fano 5-folds of index 2. There exist exactly 10 smooth toric Fano 5-folds of index 2 up to isomorphisms.

We show that a nef and big line bundle whose adjoint bundle has non-zero global sections on a nonsingular toric weak Fano 3-fold is normally generated. As a consequence, we see that any ample line bundle on a nonsingular toric waek Fano 3-fold is normally generated. As an application, we see that an ample line bundle on a Calabi-Yau hypersurface in a nonsingular toric Fano 4-fold is normally ge...

Conductance through a system consisting of a wire with side-attached quantum dots is calculated. Such geometry of the device allows to study the coexistence of quantum interference, electron correlations and their influence on conductance. We underline the differences between ”classical” Fano resonance in which the resonant channel is of single-particle nature and ”many-body” Fano resonance wit...

1. Kristina Altmann, Hyperbolic lines in unitary space. 2. John Bamberg, Transitive m-systems. 3. Barbara Baumeister, The primitive permutation groups with a regular subgroup. 4. Rieuwert Blok, Extensions of isomorphisms for affine grassmannians over F2. 5. Matthew Brown, Tetradic sets of elliptic quadrics of PG(3, q) and generalized quadrangles of order (s, s2) with Property (G). 6. Julia Brow...

An important characterization of neural spiking is the ratio of the variance to the mean of the spike counts in a set of intervals--the Fano factor. For a Poisson process, the theoretical Fano factor is exactly one. For simulated or experimental neural data, the sample Fano factor is never exactly one, but often appears close to one. In this short communication, we characterize the distribution...

We present a hybrid graphene/dielectric metasurface design to achieve strong tunable and modulated transmission at near-infrared (near-IR) frequencies. The proposed device is constituted by periodic pairs of asymmetric silicon nanobars placed over a silica substrate. An one-atom-thick graphene sheet is positioned over the all-dielectric metasurface. The in-plane electromagnetic fields are highl...

We study log canonical thresholds of effective divisors on weighted threedimensional Fano hypersurfaces to construct examples of Fano varieties of dimension six and higher having infinite, explicitly described, discrete groups of birational selfmaps.

An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.

In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.

Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain variety itself permutohedral which is a toric variety. We give complete classification Fano weak regular in type A terms combinatorics functions. In particular, we show that if anticanonical bundle nef, then it fact nef big.