Division formulas on projective varieties (Q330007)

Let \(X\) be a possibly singular closed irreducible subvariety of \(\mathbb{P}^n\). Assuming that \(\rho\in\mathbb{N}\) is larger than an explicitly defined constant, the authors prove a division-interpolation formula for sections of the line bundle \(\mathcal{O}(\rho)\) restricted to \(X\). This formula is applied to obtain explicit representations of solutions to various polynomial division problems on the affine part of \(X\).