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arXiv · 2304.09955

Double covers of smooth quadric threefolds with Artin-Mumford obstructions to rationality

Alexandra Kuznetsova
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Abstract

We study obstructions to rationality on a nodal Fano threefold $M$ that is a double cover of a smooth quadric threefold ramified over an intersection with a quartic threefold in $\mathbb{P}^4$. We prove that if $M$ admits an Artin--Mumford obstruction to rationality then it lies in one of three explicitly described families. Conversely, a general element of any of these families admits an Artin--Mumford obstruction to rationality. Only one of these three families was known before; other two families of nodal Fano threefolds with obstructions to rationality are new.

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Alexandra Kuznetsova. 2023-04-19. Double covers of smooth quadric threefolds with Artin-Mumford obstructions to rationality. https://arxiv.org/abs/2304.09955

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