BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Corey Brooke (University of Oregon) DTSTART:20221027T223000Z DTEND:20221027T233000Z DTSTAMP:20260422T054030Z UID:SFUQNTAG/74 DESCRIPTION:Title: Abelian surface fibrations and lines on cubic fourfolds\nby Corey Br ooke (University of Oregon) as part of SFU NT-AG seminar\n\n\nAbstract\nIf X is a cubic fourfold (i.e. a hypersurface of degree three in P^5)\, then its Fano variety of lines F is an irreducible symplectic variety of dimen sion four. Over the complex numbers\, tools from hyperkähler geometry rev eal that F only admits a nontrivial morphism to a lower-dimensional variet y when X contains certain "special" algebraic surfaces. In this talk\, we consider the case when X contains a plane: it turns out that F is biration al to another irreducible symplectic variety admitting a morphism to P^2 w hose general fiber is an abelian surface. We will show the key geometric i ngredients involved in this construction and describe some of its arithmet ic when the ground field is not closed.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/74/ END:VEVENT END:VCALENDAR