• Corpus ID: 248299798

On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties

@inproceedings{Chen2022OnTK,
  title={On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties},
  author={Jungkai Alfred Chen and Hsueh-Yung Lin and Keiji Oguiso},
  year={2022}
}
. We study the main open parts of the Kawaguchi–Silverman Conjecture, as-serting that for a birational self-map f of a smooth projective variety X defined over Q , the arithmetic degree α f ( x ) exists and coincides with the first dynamical degree δ f for any Q -point x of X with a Zariski dense orbit. Among other results, we show that this holds when X has Kodaira dimension zero and irregularity q ( X ) ≥ dim X − 1 or X is an irregular threefold (modulo one possible exception). We also study… 

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