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SUMMARY:Stephen Pietromonaco (University of British Columbia)
DTSTART:20220324T223000Z
DTEND:20220324T233000Z
DTSTAMP:20260422T055509Z
UID:SFUQNTAG/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/62/
 ">Enumerative Geometry of Orbifold K3 Surfaces</a>\nby Stephen Pietromonac
 o (University of British Columbia) as part of SFU NT-AG seminar\n\nLecture
  held in K-9509.\n\nAbstract\nTwo of the most celebrated theorems in enume
 rative geometry\n(both predicted by string theorists) surround curve-count
 ing for K3\nsurfaces. The Yau-Zaslow formula computes the honest number of
  rational\ncurves in a K3 surface\, and was generalized to the Katz-Klemm-
 Vafa formula\ncomputing the (virtual) number of curves of any genus. In th
 is talk\, I will\nreview this story and then describe a recent generalizat
 ion to orbifold K3\nsurfaces. One interpretation of the new theory is as p
 roducing a virtual\ncount of curves in the orbifold\, where we track both 
 the genus of the curve\nand the genus of the corresponding invariant curve
  upstairs. As one\nexample\, we generalize the counts of hyperelliptic cur
 ves in an Abelian\nsurface carried out by Bryan-Oberdieck-Pandharipande-Yi
 n. This is work in\nprogress with Jim Bryan.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/62/
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