Related papers: Five embeddings of one simple group

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.

Let $X$ be a K3 surface with Picard number 1 and genus $g$, such that $g\not\equiv 3 \mod 4$. In this paper, we show that $X$ is a Fano visitor, i.e., there is a smooth Fano variety $Y$ and an embedding $D^b(X)\hookrightarrow D^b(Y)$ given…

We announce a factorization result for equivariant birational morphisms between toric 4-folds whose source is Fano: such a morphism is always a composite of blow-ups along smooth invariant centers. Moreover, we show with a counterexample…

In this paper we consider Q-Fano 3-fold weighted complete intersections of codimension 2 in the 85 families listed in the Iano-Fletcher's list and determine which cycle is a maximal center or not. For each maximal center, we construct…

This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for non-simply connected embedded minimal surfaces of any given fixed genus. The…

In this paper we present an effective method for linearizing rational varieties of codimension at least two under Cremona transformations, starting from a given parametrization. Using these linearizing Cremonas, we simplify the equations of…

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 prove that every non-trivial structure of a rationally connected fibre space (and so every structure of a Mori-Fano fibre space) on a general (in the sense of Zariski topology) hypersurface of degree $M$ in the $(M+1)$-dimensional…

This note is devoted to a special Fano fourfold defined by a four-dimensional space of skew-symmetric forms in five variables. This fourfold appears to be closely related with the classical Segre cubic and its Cremona-Richmond configuration…

We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetric matrices, and can be seen as higher-dimensional analogues…

Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…

We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which…

We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a reductive group G which measures how nice an equivariant…

We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.

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.

We address the following question: When an affine cone over a smooth Fano threefold admits an effective action of the additive group? In this paper we deal with Fano threefolds of index 1 and Picard number 1. Our approach is based on a…

Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree $d \in \{2,3,4,5\}$ and crepant categorical resolutions of the nontrivial…

We explain an effective Kawamata boundedness result for Mori-Fano 3-folds. In particular, we describe a list of 39,550 possible Hilbert series of semistable Mori-Fano 3-folds, with examples to explain its meaning, its relationship to known…

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six…

We show that, for a $\mathbb Q$-Fano threefold $X$ of Fano index 7, the inequality $\dim |-K_X| \ge 15$ implies that $X$ is isomorphic to one of the following varieties $\mathbb P (1^2,2,3)$, $X_6 \subset \mathbb P (1,2^2,3,5)$ or $X_6…