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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

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.

Keywords

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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