Principal N-Bundles for N an Extension of a Finite Group by an Abelian Group

Abstract

Consider an extension 0 → T → N → W → 0 of a finite group W by an abelian group T. Let X be a smooth projective complex curve. Let ℳ _X (N) denote the moduli space of principal N-bundles on the curve X. We give a precise description of the fiber of the quotient by T map q _T : ℳ _X (N) → ℳ _X (W) as a torsor over an abelian variety, namely, the Prym–Donagi variety. We also prove a result on Mumford groups.

Key Words:

• Abelian variety
• Abelianisation program
• Algebraic groups
• G-Bundles
• Spectral sequence

2000 Mathematics Subject Classification:

• 14H40
• 14H60

ACKNOWLEDGMENTS

I wish to thank my advisor Christian Pauly for his advices and help in the preparation of this paper and my thesis. Je remercie le Département de Mathématiques d'Université Montpellier-II où ce travail a été effectué et ses membres qui m'ont aidé de nombreuses manières. I thank the Chennai Mathematical Institute where this work was finally finished.

Notes

Communicated by S. Kleiman