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A criterion for virtual global generation

Indranil BiswasA. J. Parameswaran — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a smooth projective curve defined over an algebraically closed field k , and let F X denote the absolute Frobenius morphism of X when the characteristic of k is positive. A vector bundle over X is called virtually globally generated if its pull back, by some finite morphism to X from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of k is positive, a vector bundle E over X is virtually globally generated if and only if ( F X m ) * E E a E f for...

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