Pure Hodge structure: Difference between revisions

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Definition

Let $H$ be an Abelian group. A pure Hodge structure of weight $n$ on $H$ is a decomposition of $H\otimes \mathbb {C}$ as a direct sum of components $H^{p,q}$ where $p,q$ are nonnegative and $p+q=n$ , such that ${\overline {H^{p,q}}}=H^{q,p}$ .

External links

Wikipedia page

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 ==Definition==
-Let <math>H</math> be an [[Abelian group]]. A '''pure Hodge structure''' of weight <math>n</math> on <math>H</math> is a decomposition of <math>H \otimes \C</math> as a direct sum of components <math>H^{p,q}</math> where <math>p,q</math> are nonnegative and <math>p + q = n</math>, such that <math>\overline{H^{p,q}} = H^{q,p}</math>.
+Let <math>H</math> be an [[Abelian group]]. A '''pure Hodge structure''' of weight <math>n</math> on <math>H</math> is a decomposition of <math>H \otimes \mathbb{C}</math> as a direct sum of components <math>H^{p,q}</math> where <math>p,q</math> are nonnegative and <math>p + q = n</math>, such that <math>\overline{H^{p,q}} = H^{q,p}</math>.
 ==External links==
 * {{wp|Hodge_structure}}