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Journal of the Ramanujan Mathematical Society

Volume 29, Issue 1, March 2014  pp. 93–117.

Criteria for existence of stable parahoric SOn, Spn and Spin bundles on P1

Authors Yashonidhi Pandey
Author institution: Indian Institute of Science Education and Research, Mohali Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306, India

Summary:  Let p: Y → X be a Galois cover of smooth projective curves over C with Galois group γ. This paper is devoted to the study of principal orthogonal and symplectic bundles E on Y to which the action of γ on Y lifts. We notably describe them intrinsically in terms of objects defined on X and call these objects parahoric bundles. We give necessary and sufficient conditions for the non-emptiness of the moduli of stable (and semi-stable) parahoric special orthogonal, symplectic and spin bundles on the projective line P1.


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