Related papers: Cylinders in Fano varieties
We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality.
We produce a list of 64 families of Fano fourfolds of K3 type, extracted from our database of at least 634 Fano fourfolds constructed as zero loci of general global sections of completely reducible homogeneous vector bundles on products of…
We show that the Picard rank is constant in families of Fano varieties (in arbitrary characteristic) and we moreover investigate the constancy of the index.
In this paper, we will give a precise formula to compute delta invariants of projective bundles and projective cones of Fano type.
We prove results about 1-cycles on certain Fano varieties using techniques that rely on rational curves. Firstly, we show that Fano weighted complete intersections with index bigger than half their dimension have trivial first Griffiths…
This note outlines some first steps in the classification of Fano manifolds for which $c_1^2-2c_2$ is positive or nef.
The Fano Resonance, involving the mixing between a quasi-bound `discrete' state of an inelastic channel lying in the continuum of scattering states belonging to the elastic channel, has several subtle features. The underlying ideas have…
We prove that the Fano variety of lines of a cuspidal cyclic cubic fourfold is a symplectic variety with transversal A2-singularities and we study the properties of the nonsymplectic order three automorphism induced by the covering…
We construct new families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of form $Z\times A^1$, where $Z$ is a quasiprojective variety. The affine cones over such a fourfold admit effective…
Several topics related to quantum spin models of Calogero-Sutherland type, partially solvable spin chains and Polychronakos's "freezing trick" are rigorously studied.
We complete the study of birational geometry of Fano fiber spaces $\pi\colon V\to {\mathbb P}^1$, 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…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete…
We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal…
We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional toric Fano manifolds, all four-dimensional…
Single particle resonances in quantum wires are generally Fano resonances. In case of Fano resonances, the scattering phase shift in some channels show sharp phase drops and that in the other channels do not. Phase shift in a particular…
We completely classify toric weakened Fano 3-folds, that is, smooth toric weak Fano 3-folds which are not Fano but are deformed to smooth Fano 3-folds. There exist exactly 15 toric weakened Fano 3-folds up to isomorphisms.
In this paper give a survey about L^2-invariants focusing on 3-manifolds.