複素解析幾何セミナー

過去の記録 ~07/20次回の予定今後の予定 07/21~

開催情報 月曜日 10:30~12:00 数理科学研究科棟(駒場) 128号室
担当者 平地 健吾, 高山 茂晴, 細野 元気

2018年04月23日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室
奥山裕介 氏 (京都工芸繊維大学)
Degeneration and bifurcation of quadratic endomorphisms of $\mathbb{P}^2$ towards a Hénon map (JAPANESE)
[ 講演概要 ]
The space of quadratic holomorphic endomorphisms of $\mathbb{P}^2$ (over $\mathbb{C}$) is canonically identified with the complement of the zero locus of the resultant form on $\mathbb{P}^{17}$, and all Hénon maps, which are (the only) interesting ones among all the quadratic polynomial automorphisms of $\mathbb{C}^2$, live in this zero locus.

We will talk about our joint work with Fabrizio Bianchi (Imperial College, London) on the (algebraic) degeneration of quadratic endomorphisms of $\mathbb{C}^2$ towards Hénon maps in terms of Berteloot-Bianchi-Dupont's bifurcation/unstability theory of holomorphic families of endomorphisms of $\mathbb{P}^k$, which mostly generalizes Mañé-Sad-Sullivan, Lyubich, and DeMarco's seminal and similar theory on $\mathbb{P}^1$.

Some preliminary knowledge on ergodic theory and pluripotential theory would be desirable, but not be assumed.