Related papers: Fano threefolds in positive characteristic IV
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 smooth Fano threefolds with infinite automorphism groups.
Over an algebraically closed field of positive characteristic, we classify smooth Fano threefolds of Picard number one whose anti-canonical linear systems are not very ample. Furthermore, we also prove that an anti-canonically embedded Fano…
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.
In this notes we classify toric Fano 4-folds having positive second Chern Character.
We classify Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.
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 find all K-stable smooth Fano threefolds in the family No. 2.22.
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
We prove that all smooth Fano threefolds of rank 4 and degree 24 are K-stable.
A Fano surface of a smooth cubic threefold X in P^4 parametrizes the lines on X. In this note, we prove that a Fano surface satisfies the Tate conjecture over a field of finite type over the prime field and characteristic not 2.
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 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.
We study the Picard variety of the Fano surface of nodal and mildly cuspidal cubic threefolds in arbitrary characteristic by relating divisors on the Fano surface to divisors on the symmetric product of a curve of genus 4.
By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of smoothable Fano 3-folds.
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 describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.
We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$.
We give a classification of smooth Fano fourfolds such that the base scheme of the anticanonical system is a smooth surface. As a consequence we show that there are exactly 22 deformation families of such manifolds and they are all obtained…