Mixed Hodge structures

By C. Peters, J. Fourier, Jozef Steenbrink. 2008

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Symmetric products of mixed Hodge modules (2010, background): “rove only a weaker version of loc. cit. by Proposition (2.8) below.) By Steenbrink [St], there is Hodge theory for compact complex V-manifolds with a Ka¨hler desingularization. (This is reproduced in [PS], Section 2.5.) As for the relation with the theory of Hodge modules, we ﬁrst note the following”
Topology of Hitchin systems and Hodge theory of character varieties (2010, background): “(See the textbook [47] for a comprehensive treatment of mixed Hodge theory.”
The Torelli locus and special subvarieties (2011, background): “For a more comprehensive treatment we refer to [19] and [67].”
Introduction to the log minimal model program for log canonical pairs (2009, unknown): “The recent book [PS] may be useful.”
Boundary complexes and weight filtrations (2011, background): “Exact Sequence of a Pair ([PS08], Proposition 5.”
Matroid Theory for Algebraic Geometers (2014, result): “k) → Z[u] to be the compactlysupported χy-characteristic given on varieties by χc y(X) = X p,q X m (−1)mhp,q(Hm(X))up where the Hodge numbers are taken with respect to Deligne’s mixed Hodge structure [75]. Since χc y([k]) = u−1, we derive the following result of Orlik-Solomon [70] as proved in [2, 5”
Mixed Hodge polynomials of character varieties (2006, background): “Its basic properties are as follows (for proofs see [58]):”