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SUMMARY:Christopher Manon (U. Kentucky)
DTSTART:20220909T140000Z
DTEND:20220909T150000Z
DTSTAMP:20260423T021058Z
UID:LAGARTOS/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGARTOS/46/
 ">Toric vector bundles and tropical geometry</a>\nby Christopher Manon (U.
  Kentucky) as part of (LAGARTOS) Latin American Real and Tropical Geometry
  Seminar\n\n\nAbstract\nI’ll give an overview of some recent work on the
  geometry of projectivized toric\nvector bundles. A toric vector bundle is
  a vector bundle over a toric variety equipped\nwith an action by the defi
 ning torus of the base. As a source of examples\, toric\nvector bundles an
 d their projectivizations provide a rich class of spaces that still\nmanag
 e to admit a combinatorial characterization. I’ll begin with a recent cl
 assification result which shows that a toric vector bundle can be captured
  by an\narrangement of points on the Bergman fan of a matroid defined by D
 iRocco\, Jabbusch\, and Smith in their work on ”the parliament of polyto
 pes” of a vector bundle.\nThen I’ll describe how to extract geometric 
 information of the projectivization of\nthe toric vector bundle when this 
 data is nice. I will focus primarily on the Cox\nring of the bundle\, and 
 the question of whether or not the bundle is a Mori dream\nspace. Then I
 ’ll describe how these properties interact with natural operations on\nt
 oric vector bundles. This involves the geometry of the closely related cla
 ss of toric\nflag bundles and tropical flag varieties. This is joint work 
 with Kiumars Kaveh and\nCourtney George.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/46/
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