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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 ...
Independent parameters for special instanton bundles on P^{2n+1} (Pre-published Version)
(Elsevier, 2011)
Motivated by Yang-Mills 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 ...
The moduli stack of vector bundles on a curve (Pre-published 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.
Einstein-Hermitian connection on twisted Higgs bundles (Pre-published 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 ...
Trace forms of symbol algebras (Pre-published version)
(World Scientific Publishing Complany, 2012)
Let S be a symbol algebra. The trace form of S is computed and it is
shown how this form can be used to determine whether S is a division algebra or not.
In addition, the exterior powers of the trace form of S are computed.
The Picard group of a coarse moduli space of vector bundles in positive characteristic (Pre-published version)
(Versita, co-published 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 ...
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 ...
Analytic moduli spaces of simple sheaves on families of integral curves (Pre-print 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, ...
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.
Poincaré families of G-bundles on a curve (Pre-published version)
(Springer Verlag, 2012)
Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary and sufficient conditions for the existence of ...