There is a map $d\log:H^1(X,\mathcal{O}_X^\times)\to H^1(X,\Omega_X^1)$ taking a line bundle to it's Chern class (at least, when everything is over $\mathbb{C}$, I believe this works). An ample class is then the Chern class of an ample line bundle.
Charles Siegel
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