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SUMMARY:Rigidity of the period map up to finite covers [MPIM]
DTSTART:20260416T130000Z
DTEND:20260416T140000Z
DTSTAMP:20260417T222600Z
UID:indico-event-1215@math-events.uni-bonn.de
DESCRIPTION:Speakers: Xiyan Zhong (MPIM)\n\nMPI-Oberseminar\nThe period ma
 p is an important holomorphic map from the moduli space $M_g$ of genus g c
 urves to the moduli space $A_g$ of g-dimensional principally polarized abe
 lian varieties\, sending a curve to its Jacobian. It was shown by Farb tha
 t the period map is the unique nonconstant holomorphic map from $M_g$ to $
 A_h$ for h \\le g. In my work\, we study holomorphic maps from a certain f
 inite cover $R_g$ of $M_g$ to $A_h$ for h \\le g\, and prove that the uniq
 ue  nonconstant holomorphic map from $R_g$ to $A_h$ is the composition of
  the covering map $R_g$ to $M_g$ and the period map from $M_g$ to $A_g$.Th
 e proof is based on classifying linear representations of certain finite-i
 ndex subgroups of the mapping class group.\n \n\nhttps://math-events.uni-
 bonn.de/event/1215/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1215/
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