Department of Mathematics and Computer Studies
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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 ... 
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 ⊗ ... 
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 ... 
Torelli Theorem for the DeligneHitchin Moduli Space (PrePublished Version)
(Springer Verlag, 2009)Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let M DH (X) denote the corresponding SL(r,C) Deligne–Hitchin moduli space. We prove that the complex analytic ... 
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. 
Trace forms of Symbol Algebras(PrePublished 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. 
SU(5) heterotic Standard Model bundles (PrePublished Version)
(Springer Verlag, 2012)We construct a class of stable SU(5) bundles on an elliptically ﬁbered CalabiYau threefold with two sections, a variant of the ordinary Weierstrass ﬁbration, which admits a free involution. The bundles are invariant under ... 
The BodenHu conjecture holds precisely up to rank eight(PrePublished version)
(Springer Verlag, 2004) 
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 ... 
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 ... 
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 ... 
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. ... 
The Picard Group of a Coarse Moduli Space of Vector Bundles in Positive Characteristic(Pre Published 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 ... 
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 ... 
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 ... 
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. 
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 ... 
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 ... 
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 ... 
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 ...