Related papers: Characterizing Varieties Using Birational Transfor…

For a reductive Lie algbera over an algbraically closed field of charasteristic zero,we consider a borel subgroup $B$ of its adjoint group, a Cartan subalgebra contained inthe Lie algebra of $B$ and the closure $X$ of its orbit under $B$ in…

We call a group $G$ nilpotently Jordan of class at most $c$ $(c\in\mathbb{N})$ if there exists a constant $J\in\mathbb{Z}^+$ such that every finite subgroup $H\leqq G$ contains a nilpotent subgroup $K\leqq H$ of class at most $c$ and index…

We give a branching law for subgroups fixed by an involution. As an application we give a generalization of the Cartan-Helgason theorem and a noncompact analogue of the Borel-Weil theorem.

Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…

Let X be the variety obtained by the Weil transfer with respect to a quadratic separable field extension of a generalized Severi-Brauer variety. We study (and, in some cases, determine) the canonical dimension, incompressibility, and…

Let $k$ be a field, and let $L$ be an \'etale k-algebra of finite rank. If $a$ is a nonzero element in $k$, let $X_a$ be the affine variety defined by the norm equation $N_{L/k}(x) = a$. Assuming that $L$ has at least one factor that is a…

We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…

We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between…

We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…

Varieties of Sums of Powers describe the additive decompositions of an homogeneous polynomial into powers of linear forms. Despite their long history, going back to Sylvester and Hilbert, few of them are known for special degrees and number…

We introduce the notion of a variety (or more generally a motive) of CM-type which generalises the well known notion of abelian variety of CM-type. Just as in that particular case it will turn out that the cohomology of the variety is…

We study upper bounds on the order of automorphisms of non-singular curves $X$ satisfying at least one of the following hypothesis: 1) $X$ is an $m$-sheeted covering of exactly one non-singular curve of genus $\gamma$, where $m$ is prime;…

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…

Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…

Let $k$ be a field, $f \colon X \to Y$ a birational morphism of integral connected schemes proper over $k$ with $Y$ normal, $x \in X(k)$ lying over $y \in Y(k)$. For Tannakian categories $\cC_X \subset \Vect(X)$ and $\cC_Y \subset…

We define a bivariate polynomial for unlabeled rooted trees and show that the polynomial of an unlabeled rooted tree $T$ is the generating function of a class of subtrees of $T$. We prove that the polynomial is a complete isomorphism…

We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a…

In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.

We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…

We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root…