Mathematics – Algebraic Geometry
Scientific paper
2000-03-24
Mathematics
Algebraic Geometry
17 pages; LaTeX2e
Scientific paper
The moduli space M(n,d) is an algebraic variety parametrizing those representations of the fundamental group of a punctured Riemann surface into the Lie group SU(n) for which a loop around the boundary is sent to the n-th root of unity exp (2 \pi i d/n) multiplied by the identity matrix. If n and d are coprime it is in fact a K\"ahler manifold. One may relax the constraint and study moduli spaces M(L) parametrizing those representations for which the loop around the boundary is sent to an element conjugate to L, if L is some element in SU(n), and these are also K\"ahler manifolds for a suitable class of L. The Verlinde formula calculates the dimension of the space of holomorphic sections of certain line bundles over the spaces M(n,d) and M(L). We recall how a new proof of the Verlinde formula for M(n,d) given in joint work with Frances Kirwan may be obtained, and show how to modify this proof to obtain a proof of the variant of the Verlinde formula which applies to M(L) (the moduli space of parabolic bundles with one marked point) and to the analogous object with b marked points.
No associations
LandOfFree
The Verlinde formula for parabolic bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Verlinde formula for parabolic bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Verlinde formula for parabolic bundles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-370511