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SUMMARY:Nathan Ilten (SFU)
DTSTART:20200528T223000Z
DTEND:20200528T233000Z
DTSTAMP:20260422T053454Z
UID:SFUQNTAG/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/4/"
 >Fano schemes for complete intersections in toric varieties</a>\nby Nathan
  Ilten (SFU) as part of SFU NT-AG seminar\n\n\nAbstract\nThe study of the 
 set of lines contained in a fixed hypersurface is classical: Cayley and Sa
 lmon showed in 1849 that a smooth cubic surface contains 27 lines\, and Sc
 hubert showed in 1879 that a generic quintic threefold contains 2875 lines
 . More generally\, the set of k-dimensional linear spaces contained in a f
 ixed projective variety X itself is called the k-th Fano scheme of X. Thes
 e Fano schemes have been studied extensively when X is a general hypersurf
 ace or complete intersection in projective space.\n\n<p>In this talk\, I w
 ill report on work with Tyler Kelly in which we study Fano schemes for hyp
 ersurfaces and complete intersections in projective toric varieties. In pa
 rticular\, I'll give criteria for the Fano schemes of generic complete int
 ersections in a projective toric\nvariety to be non-empty and of "expected
  dimension". Combined with some intersection theory\, this can be used for
  enumerative problems\, for example\, to show that a general degree (3\,3)
 -hypersurface in the Segre embedding of $\\mathbb{P}^2\\times \\mathbb{P}^
 2$ contains exactly 378 lines.</p>\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/4/
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