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1
Content available remote

Holomorphic triples of genus 0

100%
Pasotti S., Prantil F.
Open Mathematics
|
2008
|
tom 6
|
nr 1
129-142
EN
Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.
2
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The Brauer group of desingularization of moduli spaces of vector bundles over a curve

81%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1300-1305
EN
Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.
3
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SUX(r, L) is separably unirational

81%
Hein G.
Open Mathematics
|
2009
|
tom 7
|
nr 1
59-60
EN
We show that the moduli space of SUX (r, L) of rank r bundles of fixed determinant L on a smooth projective curve X is separably unirational.
4
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The Picard group of a coarse moduli space of vector bundles in positive characteristic

81%
Hoffmann N.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1306-1313
EN
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,Lss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,Lss) = ℤ, identify the ample generator, and deduce that M r,Lss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive characteristic.
5
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The associated map of the nonabelian Gauss-Manin connection

81%
Chen T.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1407-1421
EN
The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.
6
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Symmetric theta divisors of Klein surfaces

62%
Okonek C., Teleman A.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1314-1320
EN
This is a slightly expanded version of the talk given by the first author at the conference Instantons in complex geometry, at the Steklov Institute in Moscow. The purpose of this talk was to explain the algebraic results of our paper Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces. In this paper we compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.
7
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Criterion for connections on principal bundles over a pointed Riemann surface

62%
Biswas I.
Complex Manifolds
|
2017
|
tom 4
|
nr 1
155-171
EN
We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.
8
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Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

62%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1157-1163
EN
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
9
Content available remote

Recent results on quiver sheaves

52%
Laudin A., Schmitt A.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1246-1279
EN
In this article, we survey recent work on the construction and geometry of representations of a quiver in the category of coherent sheaves on a projective algebraic manifold. We will also prove new results in the case of the quiver • ← • → •.
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