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SUMMARY:Counting Lines on Hypersurfaces over general fields
DTSTART:20251217T140000Z
DTEND:20251217T151500Z
DTSTAMP:20260424T050800Z
UID:indico-event-15770@indico.math.cnrs.fr
DESCRIPTION:Speakers: Felipe Espreafico Guelerman (Sorbonne Université Ci
 té\, IMJ-PRG)\n\nOne of the most famous results in enumerative geometry i
 s the fact that\, over an algebraic closed field\, there are exactly 27 li
 nes on a smooth cubic surface. One may ask however\, what happens if the f
 ield is not algebraically closed. Is there a way to get an « invariant co
 unt »\, i.e.\, a count that does not depend on the cubic? Over the reals\
 , if one counts lines with signs\, there are exactly 3 real lines. In gene
 ral. using tools from A^1 homotopy theory from Morel and Voevodsky\, we ca
 n assign a local index in the set of square classes of the field to each o
 ne of the lines\, such the sum of them is invariant. In our work\, we cons
 ider general hypersurfaces and give a geometrical interpretation for the l
 ocal indices of lines\, following ideas from Finishing and Khalarmov who w
 orked on the real case. This is joint work with Stephen McKean and Sabrina
  Pauli.\n\nhttps://indico.math.cnrs.fr/event/15770/
LOCATION:Salle Pierre Grisvard (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/15770/
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