But this flat connection is not isomorphic to the obvious flat connection on the trivial line bundle over " A " 1 ( as an algebraic vector bundle with flat connection ), because its solutions do not have moderate growth at ".
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On the other hand, if we work with holomorphic ( rather than algebraic ) vector bundles with flat connection on a noncompact complex manifold such as " A " 1 = "'C "', then the notion of regular singularities is not defined.
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The condition of regular singularities means that locally constant sections of the bundle ( with respect to the flat connection ) have moderate growth at points of " Y " X ", where " Y " is an algebraic compactification of " X ".
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