Timeline for Smooth, non-isotrivial fibration with vanishing Kodaira-Spencer map at a point
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2022 at 20:44 | vote | accept | Francesco Polizzi | ||
| Jan 25, 2022 at 20:42 | comment | added | Francesco Polizzi | Very clean explanation. Morally, since the fibres of a Kodaira fibrations have genus at least $2$ (actually, at least $3$) there is a moduli space $\mathcal{M}$ for them. If $y \in Y$, there is a germ of deformation $\mathcal{X} \to U$ of the fibre $X_y$, where $U$ is a small neighborhood of $y$ in $Y$. Then the KS map is the differential of the corresponding moduli map $U \to \mathcal{M}$, and composing with a base change of $U$ ramified at $y$ we obtain a map whose differential vanishes at $y$ (by the chain rule). Thank you for pointing this out to me. | |
| Jan 25, 2022 at 20:10 | history | answered | Nikolas Kuhn | CC BY-SA 4.0 |