School of Mathematics Seminars and Lectures
The Kawaguchi-Silverman conjecture for endomorphisms on affine surfaces.
by Dr. Buddhadev Hajra (TIFR, Mumbai)
Wednesday, March 8, 2023
from
to
(Asia/Kolkata)
at AG-77
at AG-77
Description |
Abstract: This talk is based on the preprint https://arxiv.org/pdf/2104.05339.pdf by J. Jia, T. Shibata, J. Xie, and D.-Q. Zhang. For a quasi-projective variety $X$ and a finite surjective endomorphism $f:X \longrightarrow X$ defined over $\overline{\mathbb{Q}}$, the Kawaguchi-Silverman conjecture (KSC) is a conjecture predicting the coincidence of the first dynamical degree $d_1(f)$ of $f$ and arithmetic degree $\alpha_f(P)$ at a point $P \in X$ having Zariski dense $f$-orbit. This conjecture is verified for certain algebraic varieties, but the case of an open algebraic variety is hardly verified. Assuming $X$ is a smooth affine surface such that the logarithmic Kodaira dimension of $X$ is non-negative, the authors confirm KSC (when $\deg(f) \geq 2$) in this preprint, which I will present in this talk. |