Vincenzo (University of Trento, Firenze, Italy) Ancona & Bernard (University of Paris VI Pierre et Marie Curie, Paris, France) Gaveau 
Differential Forms on Singular Varieties [PDF ebook] 
De Rham and Hodge Theory Simplified

Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of hig