Related papers: Conic bundle structures on Q-Fano threefolds
A $\mathbb Q$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of $\mathbb…
We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.
In this article, we prove that any $\Bbb Q$-factorial weak Fano 3-fold with only terminal singularities has a smoothing.
We classify toric Fano threefolds having at worst terminal singularities such that a rank of a $G$-invariant part of a class group equals one, where $G$ is a group acting on the variety by automorphisms.
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 study Fano fourfolds of K3 type with a conic bundle structure. We construct direct geometrical links between these fourfolds and hyperK\"ahler varieties. As a result we describe families of nodal surfaces that can be seen as…
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.
We prove that a weak $\mathbb{Q}$-Fano $3$-fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak…
We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.
A $\mathbb Q$-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ $(Z \ni o)$ of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We obtain…
Casual structure can take the form of cone bundles on a manifold, more general local preorders on a topological space, or simplicial orientations implicit in a simplicial set. This note takes a triangulation of a conal manifold M to mean an…
We completely classify the Q-factorial terminal toric Fano three-folds such that the sum of the squared torus invariant prime divisors is non-negative.
Generalising a classical theorem by Ueno, we prove structure results for manifolds with nef or semiample cotangent bundle.
We classify Fano threefolds with only terminal singularities whose canonical class is Cartier and divisible by 2, and satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect…
We investigate the universal cover of projective threefolds whose tangent bundle is a direct sum of subbundles in case the Kodaira dimension is not 1 and 2. We also prove results on Fano manifolds with splitting tangent bundles in any…
We give a necessary and sufficient condition for a generalized Bott manifold to be Fano or weak Fano. As a consequence we characterize Fano Bott manifolds.
Let $M$ be a smooth Fano threefold such that a canonical extension of the tangent bundle is an affine manifold. We show that $M$ is rational homogeneous.
We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss…
We obtain upper bounds on the number of singular points of factorial terminal Fano threefolds.