This paper gives a partial desingularisation construction for hyperkähler quotients and a criterion for the surjectivity of an analogue of the Kirwan map to the cohomology of hyperkähler quotients. This criterion is applied to some linear actions on hyperkähler vector spaces.

Let E be a Banach lattice and let M be a norm-closed and Dedekind σ-complete ideal of E. If E contains a lattice-isometric copy of ∞ , then E/M contains such a copy as well, or M contains a lattice copy of ∞. This is one of the consequences of more general results presented in this paper. 1. Introduction. Let E be a locally solid linear lattice (Riesz space), for example , a Banach lattice, let...

Recent developments on the Tate or Eta pairing computation over hyperelliptic curves by Duursma–Lee and Barreto et al. have focused on degenerate divisors. We present efficient methods that work for general divisors to compute the Eta paring over divisor class groups of the hyperelliptic curves Hd : y2 = x p−x+d where p is an odd prime. On the curve Hd of genus 3, we provide two efficient metho...

We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi–Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.

Abstract Stone Duality (ASD) is a direct axiomatisation of general topology, in contrast to the traditional and all other contemporary approaches, which rely on a prior notion of discrete set, type or object of a topos. ASD reconciles mathematical and computational viewpoints, providing an inherently computable calculus that does not sacrifice key properties of real analysis such as compactness...

In this paper, we first give a new definition of Ω-Dedekind complete Riesz space (E,≤) in the frame vector metric (Ω,ρ,E) and investigate relation between Dedekind our concept. Moreover, introduce contraction so called α-vector proximal mapping. Then, prove certain best proximity point theorems for such mappings spaces where is space. Thus, time, acquire results on spaces. As result, generalize...

In Artin’s work on algebraic spaces and algebraic stacks [A2], [A3], a crucial ingredient is the use of his approximation theorem to prove the algebraizability of formal deformations under quite general conditions. The algebraizability result is given in [A2, Thm 1.6], and we recall the statement now (using standard terminology to be recalled later). Theorem 1.1. (Artin) Let S be a scheme local...

Let R be a domain and K its quotient-field. For a subset S of K , let FR(S) be the set of polynomials f ∈ K[x] with f(S) ⊆ R and define the R -closure of S as the set of those t ∈ K for which f(t) ∈ R for all f ∈ FR(S). The concept of R -closure was introduced by McQuillan (J. Number Theory 39 (1991), 245–250), who gave a description in terms of closure in P -adic topology, when R is a Dedekind...

The article presents an algorithm to compute a C[t]-module basis G for a given subalgebra A over a polynomial ring R = C[x] with a Euclidean domain C as the domain of coefficients and t a given element of A. The reduction modulo G allows a subalgebra membership test. The algorithm also works for more general rings R, in particular for a ring R ⊂ C((q)) with the property that f ∈ R is zero if an...

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R = Z, and when R is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, respectively. More generally, whenever R is a Dedekind domain, we extend the...