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I'm looking for a reference for the answer to the following questions.

Let $X$ be an algebraic variety over C. When is the cup product a morphism of Mixed Hodge structures? Does $X$ have to be smooth?

I'm looking for a reference for the answer to the following questions.

Let $X$ be an algebraic variety. When is the cup product a morphism of Mixed Hodge structures? Does $X$ have to be smooth?

I'm looking for a reference for the answer to the following questions.

Let $X$ be an algebraic variety over C. When is the cup product a morphism of Mixed Hodge structures? Does $X$ have to be smooth?

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Marco Golla
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I'm looking for a reference for the answer to the following questions.

Let X$X$ be an algebraic variety. When is the cup product is a morphism of Mixed Hodge structures? Has XDoes $X$ have to be smooth? Please give me a reference about this fact. Thank you.

Let X be an algebraic variety. When the cup product is a morphism of Mixed Hodge structures? Has X to be smooth? Please give me a reference about this fact. Thank you.

I'm looking for a reference for the answer to the following questions.

Let $X$ be an algebraic variety. When is the cup product a morphism of Mixed Hodge structures? Does $X$ have to be smooth?

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Mixed Hodge structure and cup product

Let X be an algebraic variety. When the cup product is a morphism of Mixed Hodge structures? Has X to be smooth? Please give me a reference about this fact. Thank you.