Related papers: Fano generalized Bott manifolds
We prove that a weak Fano manifold has unobstructed deformations. For a general variety, we investigate conditions under which a variety is necessarily obstructed.
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.
We prove that maximal log Fano manifolds are generalized Bott towers. As an application, we prove that in each dimension, there is a unique maximal snc Fano variety satisfying Friedman's d-semistability condition.
We classify complex projective manifolds $X$ for which there exists a point $a$ such that the blow-up of $X$ at $a$ is Fano.
In this paper, we introduce the notion of toric special weak Fano manifolds, which have only special primitive crepant contractions. We study the structure of them, and in particular completely classify smooth toric special weak Fano…
We prove a characterization of Fano type varieties.
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 give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph.
Let $G$ be a connected simply connected semisimple complex algebraic group and $P\, \subset\, G$ a parabolic subgroup. We give a necessary and sufficient condition for a line bundle -- on the blow-up of the generalized flag variety $G/P$…
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.
We consider a smooth projective morphism between smooth complex projective varieties. If the source space is a weak Fano (or Fano) manifold, then so is the target space. Our proof is Hodge theoretic. We do not need mod $p$ reduction…
We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.
We obtain a sufficient condition for a Fano threefold with terminal singularities to have a conic bundle structure.
We classify Q-Fano threefolds of Fano index > 2 and big degree.
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.
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
Based on the former parts, we classify smooth Fano threefolds of positive characteristic.
In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we…
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a building set to be weak Fano in terms of the building set.