Canonical Projectivization of Algebraic Varieties in Characteristic Zero

We construct a canonical projectivization of every smooth proper algebraic variety $X$ in characteristic zero. Once a principalization procedure is fixed, the construction gives a finite sequence of blowups in smooth centers with smooth projective endpoint, natural under semilinear isomorphisms and preserving the quasi-projective core, the intersection of all maximal quasi-projective open subsets. At each stage we select finitely many ideals near the generic points of the image in $X$ of the boundary of a maximal quasi-projective open. Principalizing their product strictly lowers the dimension of that image. The selection is defined intrinsically, without a polarization or a chosen projective modification; a Hilbert scheme argument proves its finiteness. Naturality embeds the automorphism group in that of a smooth projective variety of the same dimension. We then extend the construction to smooth proper integral algebraic spaces, obtaining canonical projectivizations of all compact connected Moishezon manifolds.