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arXiv · 1806.05771

The Voisin map via families of extensions

Huachen Chen
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Abstract

We prove that given a cubic fourfold $Y$ not containing any plane, the Voisin map $v: F(Y)\times F(Y) \dashrightarrow Z(Y)$ constructed in \cite{Voi}, where $F(Y)$ is the variety of lines and $Z(Y)$ is the Lehn-Lehn-Sorger-van Straten eightfold, can be resolved by blowing up the incident locus $\Gamma \subset F(Y)\times F(Y)$ endowed with the reduced scheme structure. Moreover, if $Y$ is very general, then this blowup is a relative Quot scheme over $Z(Y)$ parametrizing quotients in a heart of a Kuznetsov component of $Y.$

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Huachen Chen. 2018-06-15. The Voisin map via families of extensions. https://arxiv.org/abs/1806.05771

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