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On the Exceptional Principal Bundles Over a Surface
Author(s) -
Bhosle Usha N.,
Biswas Indranil
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002789
Subject(s) - mathematics , surface (topology) , pure mathematics , genus , abelian group , principal (computer security) , projective test , principal bundle , simple (philosophy) , vector bundle , mathematics subject classification , zero (linguistics) , algebra over a field , geometry , philosophy , linguistics , botany , epistemology , computer science , biology , operating system
Let G be a simple simply connected complex Lie group. Some criteria are given for the nonexistence of exceptional principal G ‐bundles over a complex projective surface. As an application, it is shown that there are no exceptional G ‐bundles over a surface whose arithmetic genus is zero or one. It is also shown that there are no stable exceptional G ‐bundles over an abelian surface. 2000 Mathematics Subject Classification 32L20, 14J60.