Splitting Bundles Over Hereditary Orders

ABSTRACT

Let A be a hereditary order on the projective line which ramifies at 2 or fewer points. We show that any locally projective A-module is a direct sum of minimal rank locally projective A-modules. Furthermore, we show that this property fails for all other hereditary orders on smooth projective curves.

Throughout, all objects and maps are assumed to be defined over some algebraically closed base field k.

Key Words:

• Moduli of vector bundles

Mathematics Subject Classification:

• Primary 14H60
• Secondary 16R20
• 16H05

Notes

^#Communicated by J. Alev.