Differential operators and flat connections on a Riemann surface.
Generalized transversely projective structure on a transversely holomorphic foliation.
A criterion for the existence of a flat connection on a parabolic vector bundle.
On the principal bundles over a flag manifold.
The line bundles on moduli stacks of principal bundles on a curve.
Rational real algebraic models of topological surfaces.
A remark on Hodge cycles on moduli spaces of rank 2 bundles over curves.
Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space
The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.
On the Hodge cycles of Prym varieties
We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.
Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any...
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.
Criterion for connections on principal bundles over a pointed Riemann surface
We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.
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Canonical generators of the cohomology of moduli of parabolic bundles on curves.
Invariant connections and invariant holomorphic bundles on homogeneous manifolds
Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when...
A Torelli theorem for moduli spaces of principal bundles over a curve
Let and be compact Riemann surfaces of genus , and let and be nonabelian reductive complex groups. If one component of the coarse moduli space for semistable principal –bundles over is isomorphic to another component , then is isomorphic to .
Holomorphic Cartan geometries and rational curves
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.
Higgs bundles and representation spaces associated to morphisms
Let be a connected reductive affine algebraic group defined over the complex numbers, and be a maximal compact subgroup. Let , be irreducible smooth complex projective varieties and an algebraic morphism, such that is virtually nilpotent and the homomorphism is surjective. Define where is the adjoint action. We prove that the geometric invariant theoretic quotient admits a deformation retraction to . We also show that the space of conjugacy classes of almost commuting elements...
The Brauer group of desingularization of moduli spaces of vector bundles over a curve
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.
Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves
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.
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