Related papers: Affine Sieve

According to the Markus conjecture, closed flat affine manifolds with parallel volume should be complete. We show it is the case for three-manifolds when the holonomy centralizes an affine transformation preserving the volume. It is notably…

We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field $k$ of characteristic $0$. We determine the Brauer group over the algebraic closure as a Galois module…

In \cite{MW}, B. Moonen and the author defined a new invariant, called $F$-Zips, of certain varieties in positive characteristics. We showed that the isomorphism classes of these invariants can be interpreted as orbits of a certain variety…

A number of conditions were found under which a sharply doubly transitive permutation group has an abelian normal divider.

We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x $\in$ D | a $\le$ b $\lor$ x} has a countable coinitial subset, such that D does not carry any binary operation -…

We study the interaction between Fourier-Mukai transforms and perverse filtrations for a certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the "Perverse $\supset$ Chern" phenomenon for these…

One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to…

Let $a_{i1}x_1+\cdots+a_{ik}x_k=0$, $i\in[m]$ be a balanced homogeneous system of linear equations with coefficients $a_{ij}$ from a finite field $\mathbb{F}_q$. We say that a solution $x=(x_1,\ldots, x_k)$ with $x_1,\ldots, x_k\in…

Let W be an irreducible, finitely generated Coxeter group. The geometric representation provides an discrete embedding in the orthogonal group of the so-called Tits form. One can look at the representation modulo the kernel of this form; we…

For systems with a finite number of degrees of freedom, it is shown in [arXiv:hep-th/0303014] that first class constraints are Abelianizable if the Faddeev-Popov determinant is not vanishing for some choice of subsidiary constraints. Here,…

Let A be an abelian surface over a fixed number field. If A is principally polarised, then it is known that the order of the Tate-Shafarevich group of A must, if finite, be a square or twice a square. The situation for A not principally…

We apply the BFFT formalism to a prototypical second-class system, aiming to convert its constraints from second- to first-class. The proposed system admits a consistent initial set of second-class constraints and an open potential function…

Brzezi\'nski's trusses are ``ring-like'' algebraic structures in which the addition is replaced with an abelian heap operation and the binary product satisfies a natural distributivity rule of the ternary product. The question of how to…

It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of…

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a…

Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, known as the {\it Zimmer program}. When the group is too large…

Smooth Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical…

For a smooth quasi-affine variety $X$, the affine closure $\overline{T^*X} := \text{Spec}(\mathbb{K}[T^*X])$ contains $T^*X$ as an open subset, and its smooth locus carries a symplectic structure. A natural question is whether…

We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This construction plays an important role in establishing the relation…

The inductive blockwise Alperin weight condition is a system of conditions whose verification for all non-abelian finite simple groups would imply the blockwise Alperin weight conjecture. We establish this condition for the groups $G_2(q)$,…