GIT STABILITY OF HENON MAPS

초록

In this paper we study the locus of generalized degree d Henon maps in the parameter space Rat(d)(N )of degree d rational maps P-N -> P-N modulo the conjugation action of SLN+1. We show that Henon maps are never in the GIT stable locus, that they are in the GIT unstable locus if d >= 3, and that they are in the strictly GIT semistable locus if N = d = 2. We also give a general classification of all unstable maps in Rat(2)(2).

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