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THE CRITICAL PODS OF PLANAR QUADRATIC POLYNOMIAL MAPS OF TOPOLOGICAL DEGREE 2

이종규|Sang-Min Lee|Misong Chang|Sunyang Ko
대한수학회 (The Korean Mathematical Society)|2023.05|대한수학회보 (Bulletin of the KMS)|제60권 제3호|pp. 659-675|DOI 10.4134/BKMS.b220292

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키워드

fixed pointcritical pointCritical podquadratic polynomial mapmoduli spaceconjugacy classdynamical Mordell-Lang conjecturesemistable maps
주제분류수학

초록

{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 \emph{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.

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 \emph{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.

참고문헌 (16)

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