Related papers: Fano threefolds with infinite automorphism groups

The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic…

We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality.

We study finite subgroups of outer automorphisms of free products. We give upper bounds for the orders of these finite subgroups as well as bounds for the orders of individual torsion outer automorphisms under some (necessary) conditions…

We consider 3-subgroups in groups of birational automorphisms of rationally connected threefolds and show that any 3-subgroup can be generated by at most five elements. Moreover, we study groups of regular automorphisms of terminal Fano…

We study smoothings of Fano threefolds. We prove that the Picard number remains constant in the case of terminal Gorenstein singularities.

We classify Fano polygons with finite mutation class. This classification exploits a correspondence between Fano polygons and cluster algebras, refining the notion of singularity content due to Akhtar and Kasprzyk. We also introduce…

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

In this article, we prove that any $\Bbb Q$-factorial weak Fano 3-fold with only terminal singularities has a smoothing.

We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.

We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these…

We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.

We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…

We classify (up to affine equivalence) all 7-dimensional flat manifolds with a cyclic holonomy group.

We study Calabi--Yau 3-folds with infinitely many divisorial contractions. We also suggest a method to describe Calabi--Yau 3-folds with the infinite automorphism group.

In this note, we classify smooth equivariant compactifications of $\mathbb{G}_a^n$ which are Fano manifolds with index $\geq n-2$.

Let $\mathcal{F}(n)$ be the set of smooth Fano $n$-polytopes up to unimocular equivalence. In this paper, we consider the F-equivalence or I-equivalence classes for $\mathcal{F}(n)$ and introduce F-isolated or I-isolated smooth Fano…

Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the diffeomorphism group of $M$ is of finite type and has finitely generated homotopy groups…

In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.