Related papers: A note on Fano manifolds whose second Chern charac…

In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.

In this notes we classify toric Fano 4-folds having positive second Chern Character.

In this paper, we investigate Fano manifolds whose Chern characters satisfy some positivity conditions. We prove that such manifolds admit long chains of higher order minimal families of rational curves and are covered by higher rational…

In this paper we address Fano manifolds with positive higher Chern characters. They are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, they should be covered by higher dimensional…

We show that any toric Fano manifold of dimension at most eight with the positive second Chern character is isomorphic to the projective space by using polymake.

We classify primitive Fano threefolds in positive characteristic whose Picard numbers are at least two. We also classify Fano theefolds of Picard rank two.

Based on the former parts, we classify smooth Fano threefolds of positive characteristic.

For a Fano manifold of pseudo-index at least 3 and $c_1^2-2c_2$ nef, we show irreducibility of certain spaces of curves on the Fano manifold implies the manifold is a union of rational surfaces.

In this paper, we investigate higher order minimal families $H_i$ of rational curves associated to Fano manifolds $X$. We prove that $H_i$ is also a Fano manifold if the Chern characters of $X$ satisfy some positivity conditions. We also…

In this paper we investigate Fano manifolds $X$ whose Chern characters $ch_k(X)$ satisfy some positivity conditions. Our approach is via the study of polarized minimal families of rational curves $(H_x,L_x)$ through a general point $x\in…

A simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold $G^C/P$ is provided in terms of symplectic data.

We construct examples of Fano manifolds, which are defined over a field of positive characteristic, but not over $\com$.

We classify Fano manifolds X containing a divisor E isomorphic to projective space such that the normal bundle $N_{E/X}$ is strictly negative.

We classify Q-Fano threefolds of Fano index > 2 and big degree.

We classify Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.

This note continues our previous work on special secant defective (specifically, conic connected and local quadratic entry locus) and dual defective manifolds. These are now well understood, except for the prime Fano ones. Here we add a few…

Let $X$ be a Fano manifold of Picard number one. We establish a lower bound for the second Chern class of $X$ in terms of its index and degree. As an application, if $Y$ is a $n$-dimensional Fano manifold with $-K_Y=(n-3)H$ for some ample…

The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost K{\"a}hler-Einstein metric, in a weak sense. The technique relies on a regularization theorem for closed positive (1,…

We consider extremal contractions on smooth Fano fourfolds whose second Chern character is positive. We show that such contractions can neither be of fiber type nor contract a divisor to a point.

We classify Fano fivefolds of index two which are projectivization of rank two vector bundles over four dimensional manifolds.