GROUPS OF RUSSELL TYPE OVER A CURVE

We consider groups of Russell type over a curve, which are forms of G( a)-bundle over a curve. In this article, we show that groups of Russel l type over a curve, not necessarily a Tango curve, are associated wit h locally free sheaves of rank two on the base curve. Moreover, these locally free sheaves are often stable but their Frobenius pull-backs a re not stable. We observe also pathological phenomena on completions o f groups of Russell type, namely, the existence of non-closed global d ifferential forms and the non-reducedness of the automorphism group sc heme. (C) 1998 Elsevier Science B.V. All rights reserved.