48,926 research outputs found
Projective moduli space of semistable principal sheaves for a reductive group
Let X be a smooth projective complex variety, and let G be an algebraic
reductive complex group. We define the notion of principal G-sheaf, that
generalises the notion of principal G-bundle. Then we define a notion of
semistability, and construct the projective moduli space of semistable
principal G-sheaves on X. This is a natural compactification of the moduli
space of principal G-bundles.
This is the announcement note presented by the second author in the
conference held at Catania (11-13 April 2001), dedicated to the 60th birthday
of Silvio Greco. Detailed proofs will appear elsewhere.Comment: 10 pages, LaTeX2e. Submitted to the conference proceedings of
"Commutative Algebra and Algebraic Geometry", Catania, April 200
Torelli theorem for the parabolic Deligne-Hitchin moduli space
We prove that, given the isomorphism class of the parabolic Deligne-Hitchin
moduli space over a smooth projective curve, we can recover the isomorphism
class of the curve and the parabolic points.Comment: 20 page
Automorphism group of the moduli space of parabolic bundles over a curve
We find the automorphism group of the moduli space of parabolic bundles on a
smooth curve (with fixed determinant and system of weights). This group is
generated by: automorphisms of the marked curve, tensoring with a line bundle,
taking the dual, and Hecke transforms (using the filtrations given by the
parabolic structure). A Torelli theorem for parabolic bundles with arbitrary
rank and generic weights is also obtained. These results are extended to the
classification of birational equivalences which are defined over "big" open
subsets (3-birational maps, i.e. birational maps giving an isomorphism between
open subsets with complement of codimension at least 3).
Finally, an analysis of the stability chambers for the parabolic weights is
performed in order to determine precisely when two moduli spaces of parabolic
vector bundles with different parameters (curve, rank, determinant and weights)
can be isomorphic.Comment: 99 page
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