Related papers: Cylinders in Fano varieties
We prove that a projective surface of globally $F$-regular type defined over a field of characteristic zero is of Fano type.
This article settles the question of existence of smooth weak Fano threefolds of Picard number two with small anti-canonical map and previously classified numerical invariants obtained by blowing up certain curves on smooth Fano threefolds…
Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite…
This is not a research article. This is a partial version of a mini-cours which I gave at a meeting of the ACI Jeunes Chercheurs "Dynamique des applications polynomiales" in Toulouse in november 2004. This text includes two parts of that…
An almost Fano bundle is a vector bundle on a smooth projective variety that its projectivization is an almost Fano variety. In this paper, we prove that almost Fano bundles exist only on almost Fano manifolds and study rank 2 almost Fano…
Some of the 124 toric Fano 4-folds contain abelian surfaces but most do not: in a few cases it is not known whether they do or not. By elementary methods, with a little computer help, we exclude some more possibilities.
We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau--Ginzburg models for Fano varieties; how to apply…
This work deals with the study of embeddings of toric Calabi-Yau fourfolds which are complex cones over the smooth Fano threefolds. In particular, we focus on finding various embeddings of Fano threefolds inside other Fano threefolds and…
We classify Fano polygons with finite mutation class. This classification exploits a correspondence between Fano polygons and cluster algebras, refining the notion of singularity content due to Akhtar and Kasprzyk. We also introduce…
We give conditions for a uniruled variety of dimension at least 2 to be non-solid. This study provides further evidence to a conjecture by Abban and Okada on the solidity of Fano 3-folds. To complement our results we write explicit…
It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$…
We prove a more general and precise version of the Noether-Fano inequalities for birational maps between Mori fiber spaces. This is applied to give descriptions of global canonical thresholds on Fano varieties of Picard number one.
Given a seven-element set $X = \{1,2,3,4,5,6,7\}$, there are 30 ways to define a Fano plane on it. Let us call a line of such Fano plane, that is to say an unordered triple from $X$, ordinary or defective according as the sum of two smaller…
We classify smooth Fano threefolds with infinite automorphism groups.
We show that Fano lattice polygons define a class of balanced quivers with interesting properties. The combinatorics of these quivers is related to singularities of the underlying toric Fano surface. This allows us to show that every Fano…
In the presence of direct trajectories connecting source and drain contacts, the conductance of a quantum dot may exhibit resonances of the Fano type. Since Fano resonances result from the interference of two transmission pathways, their…
We present a unifying point of view which allows to understand spectral features reported in recent experiments with two-dimensional arrays of subwavelength holes in metal films. We develop a Fano analysis of the related scattering problem…
We construct new families of smooth Fano fourfolds with Picard rank $1$ which contain open $\Bbb A^1$-cylinders, that is, Zariski open subsets of the form $Z \times \Bbb A^1$, where $Z$ is a quasiprojective variety. In particular, we show…
In this notes we classify toric Fano 4-folds having positive second Chern Character.