I am reading Voisin Hodge theory part 2. On page 37 a condition to a theorem (theorem 1.29) is written as: positive line bundle $\mathcal{O}_X(Y)= (\mathcal{I}_Y)$*. Y a smooth hyper surface of X= $\mathbb{P}_r(\mathbb{C})$.
She defines $\mathcal{I}_Y$ on page 281 of her part 1 book as: the sheaf of free $\mathcal{O}_X$-modules of rank 1 given by the holomorphic functions vanishing on $D_i$. $\mathcal{O}_X$ refers to the sheaf of germs of regular functions on X, I think.
Hopefully I've given you enough information.
Is anyone familiar with this notation? How do we go from sheaves to line bundles? What does the * and $\mathcal{O}$ mean?