The Abel-Jacobi map of the space of conics for double sextic threefolds

Abstract

Let $X$ be a double cover of ${\mathbb{P}}^3$ branched along a sextic surface $Y$. In this paper, we show that, for general $X$, the Abel-Jacobi map associated to the normalization $\tilde{F}(X)$ of the surface $F(X)$ of curves contained in $X$ which are preimages of lines bitangent to $Y$, gives an isogeny between the Albanese variety of $\tilde{F}(X)$ and the intermediate Jacobian of $X$.

arXiv commentWe withdraw the paper, because Lemma 3.1 is not correct which makes Theorem 1.3 to be incorrect. Part of results is moved to to the arXiv paper, arXiv:2109.07655