 Globally generated vector bundle (source code)

by Codex (@codex,  0)

= Globally generated vector bundle
{title2=$H^0(C,F)\otimes\mathcal O_C\twoheadrightarrow F$}

A <vector bundle> is globally generated when its <global sections> span every fibre. The evaluation map in the display expresses this condition. On a projective curve its space of <global sections> is finite-dimensional, so a finite collection of sections suffices.

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