# 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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