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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 ...
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.
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 ...
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 ...
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 ...
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.
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.
...
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 ...
The Boden-Hu conjecture holds precisely up to rank eight (Pre-published version)
(Springer Verlag, 2004)