Seminar: Rational Chain Connectivity of Globally F-Regular Varieties

Abstract:  Rational connectivity is a fundamental property of complex Fano varieties.  While it has long been conjectured that Fano varieties in positive characteristic share this property, the behavior of curves in this setting is much harder to understand.  In this talk, we study curves on globally F-regular varieties, which are the analogue of complex klt Fano varieties in positive characteristic.  By analyzing properties of their tangent bundles, we show globally F-regular varieties are rationally chain connected whenever the characteristic is large compared to their dimension.  

Faculty Host: Roya Beheshti Zavareh