学术报告（胡飞 2024.10.16）

Abstract: 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.