Seminar on Geometric Complex Analysis

Seminar information archive ~04/20Next seminarFuture seminars 04/21~

Date, time & place Monday 10:30 - 12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Kengo Hirachi, Shigeharu Takayama, Genki Hosono

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10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yûsuke Okuyama (Kyoto Institute of Technology)
Degeneration and bifurcation of quadratic endomorphisms of P^2
towards a H¥'enon map (JAPANESE)
[ Abstract ]
The space of quadratic holomorphic endomorphisms of P^2 (over C) is
canonically identified with the complement of the zero locus of the
resultant form on P^{17}, and all H¥'enon maps, which are (the only)
interesting ones among all the quadratic polynomial automorphisms of 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 C^2
towards H¥'enon maps in terms of Berteloot-Bianchi-Dupont's
bifurcation/unstability theory of holomorphic families of endomorphisms of P^k,
which mostly generalizes Ma¥~n¥'e-Sad-Sullivan, Lyubich, and DeMarco's seminal
and similar theory on P^1.

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