动力系统与分形几何讨论班——An upper bound for polynomial volume growth or Gelfand–Kirillov dimension of automorphisms of zero entropy

报  告  人：胡飞（南京大学）

报告时间：10月27日（周日）上午10点-11点

报告地点：数学楼（海纳苑2幢 ）101室

报告摘要: Let X be a smooth complex projective variety of dimension d and f an automorphism of X.Suppose that the pullback f^* of f on the real Néron–Severi space N^1(X)_R is unipotent and denote the index of the eigenvalue 1 by k+1.We prove an upper bound for the polynomial volume growth plov(f) of f, or equivalently, for the Gelfand–Kirillov dimension of the twisted homogeneous coordinate ring associated with (X, f), as follows: plov(f) \leq (k/2 + 1)d.Combining with the inequality k \leq 2(d-1) due to Dinh–Lin–Oguiso–Zhang, we obtain an optimal inequality that plov(f) \leq d^2,which affirmatively answers questions of Cantat–Paris-Romaskevich and Lin–Oguiso–Zhang.

This is joint work with Chen Jiang.