39 research outputs found
Pullback of parabolic bundles and covers of
We work over an algebraically closed ground field of characteristic zero. A
-cover of ramified at three points allows one to assign to
each finite dimensional representation of a vector bundle on with parabolic structure at the
ramification points. This produces a tensor functor from representation of
to vector bundles with parabolic structure that characterises the original
cover. This work attempts to describe this tensor functor in terms of group
theoretic data. More precisely, we construct a pullback functor on vector
bundles with parabolic structure and describe the parabolic pullback of the
previously described tensor functor.Comment: 25 page
Pushforwards of Tilting Sheaves
We investigate the behaviour of tilting sheaves under pushforward by a finite
Galois morphism. We determine conditions under which such a pushforward of a
tilting sheaf is a tilting sheaf. We then produce some examples of Severi
Brauer flag varieties and arithmetic toric varieties in which our method
produces a tilting sheaf, adding to the list of positive results in the
literature. We also produce some counterexamples to show that such a pushfoward
need not be a tilting sheaf.Comment: 21 page
The Period-Index Problem of the Canonical Gerbe of Symplectic and Orthogonal Bundles
We consider regularly stable parabolic symplectic and orthogonal bundles over
an irreducible smooth projective curve over an algebraically closed field of
characteristic zero. The morphism from the moduli stack of such bundles to its
coarse moduli space is a -gerbe. We study the period and index of this
gerbe, and solve the corresponding period-index problem.Comment: 19 pages. Complete rewrite of the previous version, including
expanded results on the moduli of parabolic G-bundles. To appear in the
Journal of Algebra. Comments welcom