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A short note on Du Bois singularities
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We study the behavior of Du~Bois singularities under base change and fiber products. For embeddable varieties in characteristic zero, we show that Du~Bois singularities descend from any field extension. We also prove that the product of a variety with rational singularities and a variety with Du~Bois singularities again has Du~Bois singularities, and we discuss the case of products of curves.
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