Timeline for moduli space of toric structures on a fixed toric variety (reference?)
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4 events
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| May 18, 2019 at 23:13 | comment | added | Allen Knutson | Demazure has a paper about the automorphism group of toric varieties, which can be nonreductive, e.g. $\mathbb P^2$ blown up at a point. Then I guess your question is about maximal tori of that automorphism group? They're still all conjugate as I recall, i.e., the resulting toric varieties are equivariantly isomorphic. Things change a great deal if you consider different toric variety structures on the same real manifold, e.g., all the even Hirzebruch surfaces are toric and complexly different but really diffeomorphic. | |
| Apr 23, 2019 at 20:31 | comment | added | Somatic Custard | @PiotrAchinger Thanks for your remarks. Can you please refer me to a further explanation of your 1)? | |
| Apr 22, 2019 at 20:38 | comment | added | Piotr Achinger | Some comments: 1) a toric str is “the same” as a divisor $D\sim -K_X$ st $\Omega_X(\log D)$ is trivial, so your moduli sp should “live” in $|-K_X|$, 2) automorphisms were computed by Cox, 3) if you fix the torus, the toric str is unique if it exists | |
| Apr 22, 2019 at 12:29 | history | asked | Somatic Custard | CC BY-SA 4.0 |