Principal bundles on elliptic fibrations

Feb, 1997
11 pages
Published in:
  • Asian J.Math. 1 (1997) 214-223
e-Print:

Citations per year

199720042011201820230246810
Abstract: (arXiv)
A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered Calabi-Yau manifold on which the heterotic theory is compactified. In this note we propose a simple algebro-geometric technique for studying the moduli spaces of principal G-bundles on an arbitrary variety X which is elliptically fibered over a base S: The moduli space itself is naturally fibered over a weighted projective base parametrizing spectral covers S~\tilde{S} of S, and the fibers are identified as translates of distinguished Pryms of these covers. In nice situations, the generic Prym fiber is isogenous to the product of a finite group and an abelian subvariety of Pic(S~)Pic(\tilde{S}).