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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.
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.
...
The Boden-Hu conjecture holds precisely up to rank eight (Pre-published version)
(Springer Verlag, 2004)
The Brauer group of moduli spaces of vector bundles over a real curve
(American Mathematical Society (AMS), 2011)
Let X be a geometrically connected smooth projective curve of
genus gX ≥ 2 over R. Let M(r, ξ) be the coarse moduli space of geometrically
stable vector bundles E over X of rank r and determinant ξ, where ξ is a real
point ...
Generalized vector bundles on curves (Pre-published version)
(de Gruyter, 1998)
In their paper [14] G. Harder and M.S. Narasimhan (and independently D. Quillen) have constructed a canonical flag of subbundles on any vector bundle on a complete smooth algebraic curve over a field. This flag measures ...
On semistable vector bundles over curves (Pre-published version)
(Elsevier, 2008)
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; ...
Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Pre-published version)
(Springer, 2010)
Let C be a connected smooth projective curve of genus g ≥ 2 over an algebraically closed field k. Consider the coarse moduli scheme Bunr,d (resp. Bunr,L) of stable vector bundles on C with rank r and degree d ∈ Z (resp. ...