Related papers: On maximally non-factorial nodal Fano threefolds
We classify Q-Fano threefolds of Fano index > 2 and big degree.
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds…
We classify smooth Fano threefolds with infinite automorphism groups.
We classify primitive Fano threefolds in positive characteristic whose Picard numbers are at least two. We also classify Fano theefolds of Picard rank two.
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 classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.
We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.
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 show that a non-toric $\mathbb{Q}$-factorial terminal Fano threefold of Picard rank $1$ and Fano index $13$ is a weighted hypersurface of degree $12$ in $\mathbb{P}(3,4,5,6,7)$.
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 classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.
We classify rank two vector bundles on a Fano threefold of Picard rank one whose projectivizations are weak Fano. We also prove the existence of examples for each case of the classification result. Our classification includes detailed…
We classify Fano threefolds with only Gorenstein terminal singularities and Picard number greater than 1 satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect to an action…
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.
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 classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein…
We study unirationality of actions of finite groups on Fano threefolds.
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…
We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.