The generalized Mukai conjecture for symmetric varieties
| Autor: | Gagliardi, Giuliano, Hofscheier, Johannes |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. 369 (2017), 2615-2649 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/6738 |
| Popis: | We associate to any complete spherical variety $X$ a certain nonnegative rational number $\wp(X)$, which we conjecture to satisfy the inequality $\wp(X) \le \operatorname{dim} X - \operatorname{rank} X$ with equality holding if and only if $X$ is isomorphic to a toric variety. We show that, for spherical varieties, our conjecture implies the generalized Mukai conjecture on the pseudo-index of smooth Fano varieties due to Bonavero, Casagrande, Debarre, and Druel. We also deduce from our conjecture a smoothness criterion for spherical varieties. It follows from the work of Pasquier that our conjecture holds for horospherical varieties. We are able to prove our conjecture for symmetric varieties. Comment: 33 pages, 2 figures, 6 tables |
| Databáze: | arXiv |
| Externí odkaz: |
|