Timeline for Can the base of an elliptically fibered Calabi-Yau threefold be an Enriques surface?
Current License: CC BY-SA 4.0
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| Aug 6, 2018 at 0:28 | comment | added | Jason Starr | Let $\nu:\widetilde{B}\to B$ be an etale, degree-$2$ cover of an Enriques surface $B$ by a K3 surface $\widetilde{B}$. Denote by $i:\widetilde{B}\to \widetilde{B}$ the associated involution. Let $(E,0)$ be an elliptic curve with involution $j:(E,0)\to (E,0).$ Let $\widetilde{X}$ be the product $\widetilde{B}\times E$ with the involution $(i,j)$. Denote the quotient by this involution as $q:\widetilde{X}\to X$. The projection $\text{pr}_{\widetilde{B}}$ on $\widetilde{X}$ induces a morphism $\pi:X\to B$ such that $\pi\circ q$ equals $\nu\circ \text{pr}_{\widetilde{B}}$. | |
| Aug 6, 2018 at 0:14 | history | asked | doetoe | CC BY-SA 4.0 |