Scholarlink

Let f be a holomorphic map of \(\mathbb {C}\mathbb {P}^2\) of degree \(d\ge 2\) , let T be its Green current and \(\mu =T\wedge T\) be its equilibrium measure. We give a new proof of a theorem due to Dujardin asserting that \(\mu \ll T\wedge \omega _{\mathbb {P}^2}\) implies \(\lambda _2=\frac{1}{2}\operatorname {Log} d\) , where \(\lambda _1 \ge \lambda _2\) are the Lyapunov exponents of \(\mu \) . Then, assuming \(\mu \ll T\wedge \omega _{\mathbb {P}^2}\) , we study slice measures \(\nu :=T\wedge dd^c|W|^2\) , where W is a holomorphic local submersion. We give sufficient conditions on the Radon-Nikodym derivative of \(\mu \) with respect to the trace measure \(T\wedge \omega _{\mathbb {P}^2}\) ensuring \(\mu =\nu \) . The involved submersion W comes from normal coordinates for the inverse branches of the iterates of f.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Slice Measures of Green Currents on \(\mathbb {C}\mathbb {P}^2\)

  • 会议论文

  • 发表日期：

    2026年

查看全文
  • Christophe Dupont,
  • Virgile Tapiero

摘要

Let f be a holomorphic map of \(\mathbb {C}\mathbb {P}^2\) of degree \(d\ge 2\) , let T be its Green current and \(\mu =T\wedge T\) be its equilibrium measure. We give a new proof of a theorem due to Dujardin asserting that \(\mu \ll T\wedge \omega _{\mathbb {P}^2}\) implies \(\lambda _2=\frac{1}{2}\operatorname {Log} d\) , where \(\lambda _1 \ge \lambda _2\) are the Lyapunov exponents of \(\mu \) . Then, assuming \(\mu \ll T\wedge \omega _{\mathbb {P}^2}\) , we study slice measures \(\nu :=T\wedge dd^c|W|^2\) , where W is a holomorphic local submersion. We give sufficient conditions on the Radon-Nikodym derivative of \(\mu \) with respect to the trace measure \(T\wedge \omega _{\mathbb {P}^2}\) ensuring \(\mu =\nu \) . The involved submersion W comes from normal coordinates for the inverse branches of the iterates of f.