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SUMMARY:Happy Uppal (University of Bristol)
DTSTART:20250528T150000Z
DTEND:20250528T160000Z
DTSTAMP:20260418T065435Z
UID:LNTS/169
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/169/">L
 ines on del Pezzo surfaces</a>\nby Happy Uppal (University of Bristol) as 
 part of London number theory seminar\n\nLecture held in K2.40\, King's Bui
 lding\, King's College London\, WC2R 2LS.\n\nAbstract\nOne of the crowning
  achievements of classical algebraic geometry is the Cayley--Salmon theore
 m\, which states that any smooth cubic surface over an algebraically close
 d field contains exactly 27 lines. Over more general fields\, however\, th
 e situation becomes more subtle: the number of lines depends on the arithm
 etic of the field. Segre classified the possible numbers of lines that can
  appear on a cubic surface over arbitrary fields and showed that all such 
 line counts can be realised over the rational numbers.\n\nIn this talk\, I
  will discuss joint work with Enis Kaya\, Stephen McKean\, and Sam Streete
 r\, in which we extend this perspective to del Pezzo surfaces---a class of
  surfaces that includes cubic surfaces. We investigate which line counts c
 an occur on del Pezzo surfaces over general fields and how these counts ar
 e influenced by the arithmetic of the field. We also explore the analogous
  question for conic bundles.\n
LOCATION:https://researchseminars.org/talk/LNTS/169/
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