Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE CRITICAL PODS OF PLANAR QUADRATIC POLYNOMIAL MAPS OF TOPOLOGICAL DEGREE 2

  • Misong Chang (Department of Mathematics Soongsil University) ;
  • Sunyang Ko (Department of Mathematics Soongsil University) ;
  • Chong Gyu Lee (Department of Mathematics Soongsil University) ;
  • Sang-Min Lee (Department of Mathematics Soongsil University)
  • Received : 2022.04.22
  • Accepted : 2022.10.28
  • Published : 2023.05.31
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Abstract

Let K be an algebraically closed field of characteristic 0 and let f be a non-fibered planar quadratic polynomial map of topological degree 2 defined over K. We assume further that the meromorphic extension of f on the projective plane has the unique indeterminacy point. We define the critical pod of f where f sends a critical point to another critical point. By observing the behavior of f at the critical pod, we can determine a good conjugate of f which shows its statue in GIT sense.

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Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2016R1D1A1B01009208 and NRF-2021R1A6A1A10044154).

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