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If you're interested in helping improve this article, I've outlined resources and data points which should be added. These additions will make a more "feature complete" article making mixed Hodge structures more accessible to a (mature enough) general mathematics audience.
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That document contains examples for relative and local cohomology, also good examples with curves: e.g. compactifying a curve with points gives an extension of mixed Hodge structures
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contains an intro with some of the related theorems. Maybe this material should be contained in a spin-off article about Milnor fibers.
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https://mathoverflow.net/questions/21483/question-about-hypercohomology-spectral-sequence-of-a-complex-of-almost-acycl
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Computing the eigenvalues for the monodromy of Milnor fibers can be done by looking at b-functions. The
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https://www.math.bgu.ac.il/~kernerdm/eTexts/Steenbrink.Mixed.Hodge.Structure.Singularities.Survey.pdf
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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529:- monodromy and weight filtration + signature of intersection forms for isolated singularities
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continuing from there the rest contains everything required for monodromy weight filtration
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good examples can be found using stable reduction, or use a
Lefschetz fibration
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https://pdfs.semanticscholar.org/d683/1f275409bb35b5704619bebe7b20a784ef16.pdf
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535:- COMPUTING MILNOR FIBER MONODROMY FOR SOME PROJECTIVE HYPERSURFACES (Dimca)
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http://geometry.ma.ic.ac.uk/acorti/wp-content/uploads/2016/07/mixedLSGNT.pdf
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514:(MULTIPLIER IDEALS, MILNOR FIBERS, AND OTHER SINGULARITY INVARIANTS) -
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Hodge Theory of maps Part I Milgiorini contains the relevant material.
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Add example of resolution of singularities for an A_n singular surface
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Elliptic curves minus points (or algebraic curves minus points) -: -->
263:{\displaystyle H^{1}(\mathbb {G} _{m};\mathbb {Z} )=\mathbb {Z} (-1)}
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pg 294 (pdf 310) of Hodge theory of
Cattani, Zein, Griffiths, Trang
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Mixed hodge structure for
Cohomology of a smooth projective variety
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Multiplier ideals, milnor fibers, and other singularity invariants
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Grothendieck Symbol gives the cycle class of a variety: checkout
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pg 265 (pg 281 in pdf) contains example of decomposition theorem
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http://www-users.math.umn.edu/~kwlan/articles/iccm-2016.pdf
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https://www.math.purdue.edu/~arapura/preprints/limitmhs.pdf
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http://www.numdam.org/article/AST_1989__179-180__145_0.pdf
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Mixed hodge module's theorem for intersection cohomology
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http://www.numdam.org/article/CM_1995__97_1-2_285_0.pdf
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Mixed Hodge
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