Browsing Department of Mathematics and Computer Studies by Title
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Algebraic dimension of twistor spaces whose fundamental system is a pencil (prepublished version)
(London Mathematical Society, 2017)We show that the algebraic dimension of a twistor space over nℂℙ2 cannot be two if n>4 and the fundamental system (that is, the linear system associated to the half‐anti‐canonical bundle, which is available on any twistor ... 
Analytic moduli spaces of simple sheaves on families of integral curves (Preprint version)
(Wiley, 2013)We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, ... 
Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope
(Athens Institute for Education and Research, 2015)The slope of the bestfit line y h x x 0 1 ( ) from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four which has exactly two real roots, one positive and ... 
The BelavinDrinfeld theorem on nondegenerate solutions of the classical YangBaxter equation
(IOP Publishing, 2010)We give a coordinate free proof of Belavin and Drinfeld's Theorem about the classi cation of nondegenerate solutions of the classical YangBaxter equation. The equivalence of different characterisations of nondegeneracy ... 
The BodenHu conjecture holds precisely up to rank eight (Prepublished version)
(Springer Verlag, 2004) 
The Brauer group of moduli spaces of vector bundles over a real curve
(American Mathematical Society (AMS), 2011)Let X be a geometrically connected smooth projective curve of genus gX ≥ 2 over R. Let M(r, ξ) be the coarse moduli space of geometrically stable vector bundles E over X of rank r and determinant ξ, where ξ is a real point ... 
Constructing isostatic frameworks for the l1 and l infinity plane
(Electronic Journal of Combinatorics, 20200612)We use a new coloured multigraph constructive method to prove that if the edgeset of a graph G = (V,E) has a partition into two spanning trees T1 and T2 then there is a map p : V → R2, p(v) = (p(v)1,p(v)2), such that ... 
Derived categories of irreducible projective curves of arithmetic genus one
(Cambridge Journals, 2006)We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact autoequivalences and the set of all tstructures ... 
EinsteinHermitian connection on twisted Higgs bundles (Prepublished Version)
(Elsevier Masson, 2010)Let X be a smooth projective variety over C. We prove that a twisted Higgs vector bundle (E , θ) on X admits an Einstein–Hermitian connection if and only if (E , θ) is polystable. A similar result for twisted vector bundles ... 
Elliptic curves – an introduction
(Irish Mathematical Society, 2007) 
Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes
(American Mathematical Society, 1999)We prove the existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes 4CP2. These are the rst examples of twistor spaces of algebraic dimension two over a ... 
Generalized vector bundles on curves (Prepublished version)
(de Gruyter, 1998)In their paper [14] G. Harder and M.S. Narasimhan (and independently D. Quillen) have constructed a canonical flag of subbundles on any vector bundle on a complete smooth algebraic curve over a field. This flag measures ... 
Geometric view of measurement errors
(Taylor and Francis, 2011)The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of ... 
Graph rigidity for unitarily invariant matrix norms
(Elsevier, 20201115)A rigidity theory is developed for barjoint frameworks in linear matrix spaces endowed with a unitarily invariant matrix norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks ... 
Homological algebra with locally compact abelian groups (Prepublished Version)
(Elsevier, 2007)In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasiabelian in the sense of J.P. Schneiders. We deﬁne a wellbehaved derived Homcomplex ... 
Independent parameters for special instanton bundles on P^{2n+1} (Prepublished Version)
(Elsevier, 2011)Motivated by YangMills theory in 4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n = 1, Okonek, Spindler and Trautmann introduced instanton bundles and special instanton bundles ... 
An investigation of the performance of five different estimators in the measurement error regression model
(Athens Institute for Education and Research, 2015)In a comprehensive paper by Riggs et al.(1978) the authors analyse the performances of numerous estimators for the regression slope in the measurement error model with positive measurement error variances >0 0 for X and ... 
Ireland's participation in the 50th international mathematical olympiad
(Irish Mathematical Society, 2009)The 50th International Mathematical Olympiad (IMO) took place in Bremen (Germany) from 12th July until 22nd July 2009. With 565 participants (59 of whom were girls) from 104 countries, this was the IMO with the largest ... 
Limitations of the least squares estimators; a teaching perspective
(Athens Institute for Education and Research, 2016)The standard linear regression model can be written as Y = Xβ+ε with X a full rank n × p matrix and L(ε) = N(0, σ2In). The least squares estimator is = (X΄X)−1XY with variancecovariance matrix Coυ( ) = σ2(X΄X)−1, where ... 
The line on moduli stacks of principal bundles on a curve
(Documenta Mathematica, 2010)Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G–bundles on any smooth projective curve over k.