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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.
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.
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 ⊗ ...