Mathematics and Computer Studies (Peer-reviewed publications): Recent submissions
Now showing items 21-40 of 45
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Elliptic curves – an introduction
(Irish Mathematical Society, 2007) -
The Belavin-Drinfeld theorem on non-degenerate solutions of the classical Yang-Baxter equation
(IOP Publishing, 2010)We give a coordinate free proof of Belavin and Drinfeld's Theorem about the classi cation of non-degenerate solutions of the classical Yang-Baxter equation. The equivalence of different characterisations of non-degeneracy ... -
Algebraic dimension of twistor spaces whose fundamental system is a pencil (pre-published 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 ... -
Moishezon twistor spaces without effective divisors of degree one (pre-published 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 ... -
Twistor spaces with a pencil of fundamental divisors
(Documenta Mathematica, 1999)In this paper simply connected twistor spaces Z containing a pencil of fundamental divisors are studied. The Riemannian base for such spaces is diffeomorphic to the connected sum nCP2 . We obtain for n 5 a complete ... -
Homological algebra with locally compact abelian groups (Pre-published Version)
(Elsevier, 2007)In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex ... -
Some moduli stacks of symplectic bundles on a curve are rational (Pre-published 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 ⊗ ... -
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 ... -
Torelli theorem for the Deligne-Hitchin moduli space (Pre-published 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 (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. -
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. -
SU(5) heterotic standard model bundles (Pre-published version)
(Springer Verlag, 2012)We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under ... -
The Boden-Hu conjecture holds precisely up to rank eight (Pre-published version)
(Springer Verlag, 2004) -
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 ... -
New examples of stable bundles on Calabi-Yau threefolds (Pre-published Version)
(Oxford University Press, 2012)In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h1 , 1 > 1. We give examples ... -
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 ... -
Rationality and Poincaré families for vector bundles with extra structure on a curve (Pre-published 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, 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 ... -
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 ...