Programm des Emmy-Noether-Seminars

Fri, 02.06.2017, 14:30

End:
Fri, 02.06.2017, 15:30
The generalized Mukai conjecture for spherical varieties
Emmy-Noether-Seminar

Speaker: Dr. Johannes Hofscheier (Magdeburg)
Host: Knop
Room: 04.363

The class of spherical varieties contains those of toric varieties, flag varieties, and symmetric spaces, and forms a remarkable and rich class of algebraic varieties with an action by an algebraic group having an open dense orbit. In this setting, we investigate the generalized Mukai conjecture, an inequality relating the pseudo-index, the dimension, and the Picard number of a smooth Fano variety. This leads us to the formulation of a new conjecture involving a certain rational invariant, which will turn out to be of independent interest, e. g., it allows us to deduce a (conjectural) combinatorial smoothness criterion for spherical varieties. We can prove our conjecture in the special case of symmetric varieties. In particular, the generalized Mukai conjecture holds in this case. This is joint work with Giuliano Gagliardi.