Related papers: Unification and projectivity in Fregean varieties
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.
Richardson varieties play an important role in intersection theory and in the geometric interpretation of the Littlewood-Richardson Rule for flag varieties. We discuss three natural generalizations of Richardson varieties which we call…
An early result in the theory of Natural Dualities is that an algebra with a near unanimity (NU) term is dualizable. A converse to this is also true: if V(A) is congruence distributive and A is dualizable, then A has an NU term. An…
We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…
Let $\mathfrak{g}$ be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well-behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie…
Two well studied invariants of a complex projective variety are the unit Euclidean distance degree and the generic Euclidean distance degree. These numbers give a measure of the algebraic complexity for "nearest" point problems of the…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories and does so by aggregating the individual classifications. We show that if $m\geq 3$, $m\geq p\geq 2$, and classifications are fuzzy, that…
We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…
We study effective global generation properties of projectivizations of curve semistable vector bundles over curves and abelian varieties.
An algebraic notion of representational consistency is defined. A theorem relating it to free actions is proved. A metrizability problem of the quotient (a shape space) is discussed. This leads to a new algebraic variety with a…
The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions…
We give a class of examples of vector bundles on a relative smooth projective curve over Spec Z such that for infinitely many prime reductions the bundle has a Frobenius descent, but the restriction to the generic fiber in characteristic…
We investigate basic properties of uniformly rational varieties, i.e. those smooth varieties for which every point has a Zariski open neighborhood isomorphic to an open subset of A^n. It is an open question of Gromov whether all smooth…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
Almost forty years ago, Connes, Feldman and Weiss proved that for measurable equivalence relations the notions of amenability and hyperfiniteness coincide. In this paper we define the uniform version of amenability and hyperfiniteness for…
It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…
This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results…
We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…
We introduce complete quotients over the projective line and prove that they form smooth projective varieties. The resulting parameter spaces coincide with the varieties constructed in [HLS11] and [Shao11]. Hence they provide modular smooth…
v2: For a projective variety defined over a finite field with $q$ elements, it is shown that as algebraic integers, the eigenvalues of the geometric Frobenius acting on $\ell$-adic cohomology have higher than known $q$-divisibility beyond…