Geodesic
Kawaguchi-Silverman conjecture for certain surjective endomorphisms
Documenta mathematica, Tome 27 (2022), pp. 1605-1642.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove the Kawaguchi-Silverman conjecture (KSC), about the equality of arithmetic degree and dynamical degree, for every surjective endomorphism of any (possibly singular) projective surface. In high dimensions, we show that KSC holds for \textit{every} surjective endomorphism of any $\mathbb{Q}$-factorial Kawamata log terminal projective variety admitting one int-amplified endomorphism, provided that KSC holds for any surjective endomorphism with the ramification divisor being totally invariant and irreducible. In particular, we show that KSC holds for \textit{every} surjective endomorphism of any rationally connected smooth projective threefold admitting one int-amplified endomorphism. The main ingredients are the equivariant minimal model program, the effectiveness of the anti-canonical divisor and a characterization of toric pairs.
Classification : 14E30, 14J50, 37P55, 08A35
Keywords: Kawaguchi-Silverman conjecture, equivariant minimal model program, int-amplified endomorphism, arithmetic degree, dynamical degree, toric variety 
@article{DOCMA_2022__27__a26,
     author = {Meng, Sheng and Zhang, De-Qi},
     title = {Kawaguchi-Silverman conjecture for certain surjective endomorphisms},
     journal = {Documenta mathematica},
     pages = {1605--1642},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a26/}
}
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Meng, Sheng; Zhang, De-Qi. Kawaguchi-Silverman conjecture for certain surjective endomorphisms. Documenta mathematica, Tome 27 (2022), pp. 1605-1642. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a26/