Related papers: Toric $G$-Fano Threefolds

We classify the non-toric, $\mathbb{Q}$-factorial, Gorenstein, Fano threefolds of Picard number one with an effective $\mathbb{K}^*$-action and maximal orbit quotient $\mathbb{P}_2$.

We characterize those countable rooted trees whose full automorphism group has uncountable strong cofinality or contains an open subgroup with ample generics.

We consider groups $G$ such that the set $[G,\varphi]=\{g^{-1}g^{\varphi}|g\in G\}$ is a subgroup for every automorphism $\varphi$ of $G$, and we prove that there exists such a group $G$ that is finite and nilpotent of class $n$ for every…

We associate to every positive braid a braid monodromy group, generalizing the geometric monodromy group of an isolated plane curve singularity. If the closure of the braid is a knot, we identify the corresponding group with a framed…

Kawakami and the author showed that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. That was a new way to analyze which varieties have nontrivial endomorphisms. In…

Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…

We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincar\'e duality.…

In this paper, we study the explicit geometry of threefolds, in particular, Fano varieties. We find an explicitly computable positive integer $N$, such that all but a bounded family of Fano threefolds have $N$-complements. This result has…

For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…

For Fano varieties of various singularities such as canonical and terminal, we construct examples with large Fano index. By low-dimensional evidence, we conjecture that our examples have the largest Fano index for all dimensions.

We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.

We classify the canonical threefold singularities that allow an effective two-torus action. This extends classification results of Mori on terminal threefold singularities and of Ishida and Iwashita on toric canonical threefold…

We analyse the local structure of the K-moduli space of Fano varieties at a toric singular K-polystable Fano 3-fold, which deforms to smooth Fano 3-folds with anticanonical volume 28 and Picard rank 4. In particular, by constructing an…

Abstract. In our previous paper arXiv:2210.16008, we show that any prime $\mathbb{Q}$-Fano 3-folds $X$ with only $1/2(1,1,1)$-singularities in certain 5 classes can be embedded as linear sections into bigger dimensional $\mathbb{Q}$-Fano…

We give a characterizaion of Gorenstein toric Fano $n$-folds with index $n-1$, which is called Gorenstein toric Del Pezzo $n$-folds, among toric varieties. In practice, we obtain a condition for a lattice $n$-polytope to be a Gorenstein…

We classify terminal simplicial reflexive d-polytopes with 3d-1 vertices. They turn out to be smooth Fano d-polytopes. When d is even there is 1 such polytope up to isomorphism, while there are 2 when d is uneven.

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of…

The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such…

We study degree of irrationality of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces that have terminal singularities.