Browsing Mathematics and Computer Studies (Peerreviewed publications) by Title
Now showing items 1736 of 40

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. 
Minimizing oblique errors for robust estimating
(Irish Mathematical Society, 2008)The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show ... 
Mitigating collinearity in linear regression models using ridge, surrogate and raised estimators
(Cogent OA, 2016)Collinearity in the design matrix is a frequent problem in linear regression models, for example, with economic or medical data. Previous standard procedures to mitigate the effects of collinearity included ridge regression ... 
Moduli schemes of generically simple Azumaya modules
(Documenta Mathematica, 2005)Let A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra. We show that generically simple torsion ... 
The moduli stack of vector bundles on a curve (Prepublished Version)
(Ramanujan Mathematical Society, 2010)This expository text tries to explain brie y and not too technically the notions of stack and algebraic stack, emphasizing as an example the moduli stack of vector bundles on an algebraic curve. 
Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Prepublished version)
(Springer, 2010)Let C be a connected smooth projective curve of genus g ≥ 2 over an algebraically closed field k. Consider the coarse moduli scheme Bunr,d (resp. Bunr,L) of stable vector bundles on C with rank r and degree d ∈ Z (resp. ... 
Moishezon twistor spaces without effective divisors of degree one (prepublished version)
(Universität Kaiserslautern, 1995)We study simply connected compact twistor spaces Z of positive type. Assuming that the fundamental linear system j \Gamma 1 2 Kj is at least a pencil, we prove the following theorem: the existence of an irreducible curve ... 
New examples of stable bundles on CalabiYau threefolds (Prepublished Version)
(Oxford University Press, 2012)In this paper we present a construction of stable bundles on CalabiYau threefolds using the method of bundle extensions. This construction applies to any given CalabiYau threefold with h1 , 1 > 1. We give examples ... 
A note on the computation of symmetric powers of hyperbolic forms and of trace froms on symbol algebras
(Scientific Advances Publishers, 2014)Let K be a field with characteristic different from 2 and let S be a symbol algebra over K. We compute the symmetric powers of hyperbolic quadratic forms over K. Also, we compute the symmetric powers of the quadratic trace ... 
On a relative FourierMukai transform on genus one fibrations
(Springer, 2006)We study relative FourierMukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and nonprojective. Grothendieck duality is used to prove a ... 
On moduli stacks of Gbundles over a curve (Prepublished version)
(Springer, 2010)Let C be a smooth projective curve over an algebraically closed eld k of arbitrary characteristic. Given a linear algebraic group G over k, let MG be the moduli stack of principal Gbundles on C. We determine the set of ... 
On semistable vector bundles over curves (Prepublished version)
(Elsevier, 2008)Let X be a geometrically irreducible smooth projective curve de ned over a eld k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that Hi(X; F E) = 0 for i = 0; ... 
The Picard group of a coarse moduli space of vector bundles in positive characteristic (Prepublished version)
(Versita, copublished with Springer Verlag., 2012)Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let Mss r,L denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant ... 
Poincaré families and automorphisms of principal bundles on a curve (Prepublished version)
(Elsevier, 2009)Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal Gbundles on C, for the existence of Poincaré families parameterized ... 
Poincaré families of Gbundles on a curve (Prepublished version)
(Springer Verlag, 2012)Let G be a reductive group over an algebraically closed ﬁeld k. Consider the moduli space of stable principal Gbundles on a smooth projective curve C over k. We give necessary and suﬃcient conditions for the existence of ... 
Rationality and Poincaré families for vector bundles with extra structure on a curve (Prepublished version)
(Oxford University Press, 2007)Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. ... 
Response surface designs using the generalized variance inflation factors
(Cogent OA, 2015)We study response surface designs using the generalized variance inflation factors for subsets as an extension of the variance inflation factors. 
Solving cubic equations in two variables
(Irish Mathematical Society, 2007)After recalling a geometric construction of all Pythagorean triples of integers, the same idea is applied to find rational solutions of cubic equations in two variables. This leads to the definition of the MordellWeil ... 
Some moduli stacks of symplectic bundles on a curve are rational (Prepublished version)
(Elsevier, 2008)Let C be a smooth projective curve of genus g ≥ 2 over a ﬁeld k. Given a line bundle L on C, let Sympl2n,L be the moduli stack of vector bundles E of rank 2n on C endowed with a nowhere degenerate symplectic form b : E ⊗ ... 
Stability of Arakelov bundles and tensor products without global sections
(Documenta Mathematica, 2003)This paper deals with Arakelov vector bundles over an arithmetic curve, i.e. over the set of places of a number field. The main result is that for each semistable bundle E, there is a bundle F such that E⊗F has at least ...