Related papers: Cylinders in Fano varieties
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
Single metallic nanorods acting as half-wave antennas in the optical range exhibit an asymmetric, multi-resonant scattering spectrum that strongly depends on both their length and dielectric properties. Here we show that such spectral…
The purpose of the present paper is to generalize Sakai's work on anticanonical models of rational surfaces to varieties of Fano type. We first prove a characterization of Fano type varieties using the singularities of anticanonical models.…
In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle…
We announce a factorization result for equivariant birational morphisms between toric 4-folds whose source is Fano: such a morphism is always a composite of blow-ups along smooth invariant centers. Moreover, we show with a counterexample…
We study a class of finite-area, infinite-type translation surfaces, and find an explicit cylinder decomposition on these surfaces which do not manifest on finite-type translation surfaces. Each cylinder decomposition contains a special…
In this note we study Fano threefolds with noncyclic torsion in the divisor class group. Since they can all be obtained as quotients of Fano threefolds, we get also all examples that can be obtained as quotients of low codimension Fanos in…
The Fano line profiles, originally discovered in the context of photoionization, have been found to occur in a large class of systems like resonators, metamaterials, plasmonics. We demonstrate the existence of such resonances in cavity…
European, Japanese, and US Neutrino Factory designs are presented. The main R&D issues, and the associated R&D programs, are discussed.
We prove the existence of Fano ladders on weak log Fano varieties of coindex less than 4, as an application of adjunction and nonvanishing.
We exhibit an example of obstructed K-polystable Fano 3-fold $X$ such that the K-moduli stack of K-semistable Fano varieties and the K-moduli space of K-polystable Fano varieties have an embedded point at $[X]$.
We show that the set of Fano varieties (with arbitrary singularities) whose anticanonical divisors have large Seshadri constants satisfies certain weak and birational boundedness. We also classify singular Fano varieties of dimension $n$…
An overview of neutrino-mixing models is presented with emphasis on the types of horizontal flavor and vertical family symmetries that have been invoked. Distributions for the mixing angles of many models are displayed. Ways to…
In this note, finite type epimorphisms of rings are characterized.
In the present paper we discuss coherent sheaves of rank > 1 whose projectivization gives rise to smooth varieties - varieties of this type are also called smooth scrolls. We prove some basic properties of these varieties and we give some…
We classify $2$-Fano horospherical varieties with Picard number $1$. We also review all the known examples of $2$-Fano manifolds and investigate the relation between the $2$-Fano condition and different notions of stability. This paper was…
Status of neutrino oscillation study is briefly reviewed. Some aspects relevant to tau physics are also described.
The goal of these lecture notes is to present the modern point of view on the classification of Fano threefolds. We tried to offer a self-consistent treatment of the topics covered. \par\medskip\noindent These notes have been published in…
Frequency and transmission spectrum of two-dimensional array of metallic rods is investigated numerically. Based on the recent analysis of the band structure of two-dimensional photonic crystal with dielectric rods [P. Marko\v{s}, Phys.…
We study unirationality of actions of finite groups on Fano threefolds.