Related papers: Fano generalized Bott manifolds

We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between…

We study Fano threefolds with~terminal singularities admitting a "minimal" action of a finite group. We prove that under certain additional assumptions such a variety does not contain planes. We also obtain an upper bounds of the number of…

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…

Fano manifolds are basic building blocks in geometry - they are, in a precise sense, atomic pieces of shapes. The classification of Fano manifolds is therefore an important problem in geometry, which has been open since the 1930s. One can…

Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We…

The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.

This paper generalizes the first author's preceding works concerning admissible functions on certain Fano manifolds. Here, we study a larger class of functions which can be less symmetric than the ones studied before. When the sup of these…

In this note we prove that any toric Fano manifold with nef tangent bundle is a product of projective spaces. In particular, it implies that Campana-Peternell conjecture hold for toric manifolds.

We study the Picard variety of the Fano surface of nodal and mildly cuspidal cubic threefolds in arbitrary characteristic by relating divisors on the Fano surface to divisors on the symmetric product of a curve of genus 4.

We study Fano manifolds $X$ admitting an unsplit dominating family of rational curves and we prove that the Generalized Mukai Conjecture holds if $X$ has pseudoindex $i_X = (\dim X)/3$ or dimension $\dim X=6$. We also show that this…

For any positive integer $k$ and any integer $n$ large enough, we construct a Fano variety $X$ with Picard number $k$ and dimension $n$ such that $((-K_X)^n)^{1/n}$ grows like $n^k/(\log n)^{k-1}$.

We show that all generalized (real) Bott manifolds which are (small covers) quasitoric manifolds over a product of simplices $\Delta^{n_1}\times\cdots\times\Delta^{n_r}\times\Delta^{1}$ are always boundaries of some manifolds. But these…

We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to…

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 prove that a smooth projective variety $X$ of dimension $n$ with strictly nef third, fourth or $(n-1)$-th exterior power of the tangent bundle is a Fano variety. Moreover, in the first two cases, we provide a classification for $X$ under…

We prove that a quasi-smooth Fano threefold hypersurface is birationally rigid if and only if it has Fano index one.

We classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.

We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the…

We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have enormously…

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…