BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chris Manon (University of Kentucky) DTSTART:20210611T143000Z DTEND:20210611T153000Z DTSTAMP:20260423T024616Z UID:ToricDeg/3 DESCRIPTION:Title: When is a (projectivized) toric vector bundle a Mori dream space?\nby Chris Manon (University of Kentucky) as part of Toric Degenerations\n\n\n Abstract\nLike toric varieties\, toric vector bundles are a rich class of varieties which admit a combinatorial description. Following the classifi cation due to Klyachko\, a toric vector bundle is captured by a subspace a rrangement decorated by toric data. This makes toric vector bundles an ac cessible test-bed for concepts from algebraic geometry. Along these line s\, Hering\, Payne\, and Mustata asked if the projectivization of a toric vector bundle is always a Mori dream space. Suess and Hausen\, and Gonza les showed that the answer is "yes" for tangent bundles of smooth\, projec tive toric varieties\, and rank 2 vector bundles\, respectively. Then Her ing\, Payne\, Gonzales\, and Suess showed the answer in general must be "n o" by constructing an elegant relationship between toric vector bundles an d various blow-ups of projective spaces\, in particular the blow-ups of ge neral arrangements of points studied by Castravet\, Tevelev and Mukai. In this talk I'll review some of these results\, and then give a new descrip tion of toric vector bundles by tropical information. This description al lows us to characterize the Mori dream space property in terms of tropical and algebraic data\, and produce new families of Mori dream spaces indexe d by the integral points in a locally closed polyhedral complex. Along t he way I'll discuss plenty of examples and some questions. This is joint work with Kiumars Kaveh.\n LOCATION:https://researchseminars.org/talk/ToricDeg/3/ END:VEVENT END:VCALENDAR