Abstract
The symmetric algebra of an ideal I may be compared to the Rees algebra via the canonical epimorphism α:Sym(I)→R(I). A necessary and sufficient criterion is given for a to be an isomorphism, and sequential conditions on the symmetric algebra are studied. Some applications are given to Proj α:ProjR(I)→Pro'j Sym(I) and to the theory of approximation complexes.
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