相关论文: Classification of 2-Fano manifolds with high index

This note outlines some first steps in the classification of Fano manifolds for which $c_1^2-2c_2$ is positive or nef.

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

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

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

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…

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

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.

In this note, we classify smooth equivariant compactifications of $\mathbb{G}_a^n$ which are Fano manifolds with index $\geq n-2$.

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…

For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a…

Let $X$ be a complex smooth Fano variety of dimension at least four. In this paper, we classify such $X$ when the pseudoindex is at least $n-2$ and the Picard number greater than one. We also discuss the relations between pseudoindex and…

We study Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X) = 1, Q-factorial terminal singularities and -K_X = 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised…

In this paper, we classify smooth toric Fano 5-folds of index 2. There exist exactly 10 smooth toric Fano 5-folds of index 2 up to isomorphisms.

We classify smooth Fano manifolds X with the Picard number $\rho_X \geq 3$ such that there exists an extremal ray which has a birational contraction that maps a divisor to a point.

We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$.

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…

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.