Now showing items 1-7 of 7
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 ...
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 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.
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 ...
On semistable vector bundles over curves (Pre-published version)
Let X be a geometrically irreducible smooth projective curve de ned over a eld k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that Hi(X; F E) = 0 for i = 0; ...
Poincaré families and automorphisms of principal bundles on a curve (Pre-published version)
Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal G-bundles on C, for the existence of Poincaré families parameterized ...
Some moduli stacks of symplectic bundles on a curve are rational (Pre-published version)
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 ⊗ ...