Timeline for "skyscraper group scheme"
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 2, 2018 at 12:22 | vote | accept | CommunityBot | ||
| Jan 17, 2018 at 19:17 | comment | added | Ariyan Javanpeykar | @ZSun This answer only answers your first question. As Laurent Moret-Bailly points out in his answer to both your questions, the above non-separated group scheme is never the automorphism group scheme of a stable curve $X$ over $S$. Even worse, if $(X,L)\to S$ is a polarized flat proper finitely presented morphism, then $Aut(X,L)\to S$ is an affine (hence separated) group scheme. Now, some varieties $X$ come with a "canonical'' (or "anti-canonical'') polarization $L$ (e.g., for stable curves of genus at least two you can take $L=\omega_X$) in which case $Aut(X) = Aut(X,L)$ is affine. | |
| Jan 17, 2018 at 17:26 | history | answered | Ariyan Javanpeykar | CC BY-SA 3.0 |