Related papers: Fano threefolds with infinite automorphism groups
We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.
We give a self-contained alternative proof of the classification of smooth prime Fano threefolds of degree 22 with infinite automorphism groups established by Kuznetsov, Prokhorov and Shramov.
Based on the former parts, we classify smooth Fano threefolds of positive characteristic.
We classify Q-Fano threefolds of Fano index > 2 and big degree.
We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.
A smooth variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We classify smooth Fano 3-folds that satisfy Condition (A).
We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$.
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 give a characterization of Fano type surfaces with large cyclic automorphisms.
We study automorphism groups of smooth quintic threefolds. Especially, we describe all the maximal ones with explicit examples of target quintic threefolds. There are exactly $22$ such groups.
We classify the possible images of the action of the group of automorphisms of a smooth Fano threefold on its Picard group. We also study the first group cohomology of the Picard group for families of smooth Fano threefolds.
It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$…
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.
Let $\mathcal{X}$ be a smooth Fano threefold over the complex numbers of Picard rank $1$ with finite automorphism group. We give numerical restrictions on the order of the automorphism group $\mathrm{Aut}(\mathcal{X})$ provided the genus…
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 Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.
We classify smooth Fano weighted complete intersections of large codimension.
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…
Fano surfaces parametrize the lines of smooth cubic threefolds. In this paper, we study their quotients by some of their automorphism sub-groups. We obtain in that way some interesting surfaces of general type.
We show that smooth well formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.