Connectivity and a Problem of Formal Geometry

Let $P=\mathbb P^m(e)\times\mathbb P^n(h)$ be a product of weighted projective spaces, and let $Δ_P$ be the diagonal of $P\times P$. We prove an algebraization result for formal-rational functions on certain closed subvarieties $X$ of $P\times P$ along the intersection $X\capΔ_P$.

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