In this book we study Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry. The main aim here is to describe their cohomology and Chow rings.

The papers in this volume reflect the recent developments in the areas of: mixed Hodge theory on the cohomology of singular and open varieties, on the rational homotopy of algebraic varieties, on the cohomology of a link, and on the vanishing cycles| L -realization of the intersection cohomology for the cases of singular varieties and smooth varieties with degenerating coefficients| applications of cubical hyperresolutions and of iterated integrals| asymptotic behavior of degenerating variations of Hodge structure| the geometric realization of maximal variations| and variations of mixed Hodge structure. N