Related papers: Notes on Fano varieties of complete intersections
One of the fundamental open questions in QFT is what kind of functions appear as Feynman integrals. In recent years this question has often been considered in a geometric context by interpreting the polynomials that appear in these…
We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. When the intersection is…
We prove that a smooth well formed Fano weighted complete intersection of codimension 2 has a nef partition. We discuss applications of this fact to Mirror Symmetry. In particular we list all nef partitions for smooth well formed Fano…
We prove that Hori--Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.
We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.
Fano mechanism is the universal explanation of asymmetric resonance appearing in different systems. We report the evidence of Fano-like resonance in selective reflection from a resonant two-level medium. We draw an analogy with the…
Fano surfaces parametrize the lines of smooth cubic threefolds. In this paper, we study their quotients by some of their automorphism sub-groups. We obtain in that way some interesting surfaces of general type.
Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetric matrices, and can be seen as higher-dimensional analogues…
Mirror symmetry predicts that bounded derived category of a smooth Fano variety is equivalent to Fukaya-Seidel category of its Landau-Ginzburg model. It is expected that fibers of Landau-Ginzburg model with ordinary double points correspond…
The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find…
A nef-partition for a weighted complete intersection is a combinatorial structure on its weights and degrees which is important for Mirror Symmetry. It is known that nef-partitions exist for smooth well-formed Fano weighted complete…
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.
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.…
The Fano resonance is a widespread wave scattering phenomenon associated with a peculiar asymmetric and ultra-sharp line shape, which has found applications in a large variety of prominent optical devices. While its substantial sensitivity…
Fano resonances are features in transmissivity/reflectivity/absorption that owe their origin to the interaction between a bright resonance and a dark (i.e., sub-radiant) narrower resonance, and may emerge in the optical properties of planar…
We study the geometry of the Fano schemes $\mathrm{\textbf{F}}_{k}(\mathrm{SD}_n^r)$ of the projective variety $\mathrm{SD}_n^r$ defined by the $r\times r$ minors of a symmetric $n\times n$ matrix filled with indeterminates. These schemes…
In this paper, we prove various results on boundedness and singularities of Fano fibrations and of Fano type fibrations. A Fano fibration is a projective morphism $X\to Z$ of algebraic varieties with connected fibres such that $X$ is Fano…
High refractive index dielectric nanostructures provide original optical properties thanks to the occurrence of size- and shape-dependent optical resonance modes. These modes commonly present a spectral overlap of broad, low-order modes…
We exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric.