Multiplicative models for configuration spaces of algebraic varieties

W. Fulton and R. MacPherson described a Sullivan dg-algebra model for the space of n-configurations of labeled points in a smooth compact complex algebraic variety X. I. Kriz then gave a simpler model that depends only on the cohomology ring of X. We construct an even simpler and substantially smaller model for this configuration space. Using this smaller model, we also define another, new dg-algebra model, for the space of n-configurations in the variety X with a point removed. Following an idea of V.G. Drinfel'd, we endow the collection of these new "punctured" models with a simplicial bigraded differential algebra structure.