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SUMMARY:Gromov-Witten Theory of Hilb(K3\,n)\, Modular forms and K3 x E. 
DTSTART:20141020T151500
DTEND:20141020T170000
DTSTAMP:20260427T212546Z
UID:df03fefb1043b3503567d48bc30c70857d9803a77274cefe3c0c23aa
CATEGORIES:Conferences - Seminars
DESCRIPTION:Georg Oberdieck (ETHZ)\nOne of the main tools in the proof of
  the Stable Pairs / Gromov-Witten correspondence for toric Calabi-Yau thre
 efolds is a correspondence between the relative GW theory of P1 x S and th
 e genus 0 GW theory of Hilb(S\,n)\, where S is the two-dimensional affine 
 plane and Hilb(S\,n) is its Hilbert scheme of points. A natural and open q
 uestion is if such a correspondence exist for other\, in particular compac
 t\, surfaces S as well.\nIn this talk\, we will consider this question in 
 the case where S is a K3 surface. First\, i will first present recent resu
 lts on the genus 0 GW theory of Hilb(S\,n) the Hilbert scheme of points of
  S. These results lead to conjectures about the full genus 0 GW theory of 
 Hilb(S\,n) (in the primitive case).\nSecond\, i will explain a conjecture 
 that a correspondence to P1 x S should exist and state its particular form
 . As an outcome\, we obtain predictions for the GW Theory of K3xE in terms
  of a Siegel modular form\, the Igusa cusp form. The second part is joint 
 work with R. Pandharipande.
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STATUS:CONFIRMED
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