Geodesic
Kawaguchi–Silverman conjecture for certain surjective endomorphisms
Documenta mathematica, Tome 27 (2022), pp. 1605-1642 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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 every surjective endomorphism of any 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 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.
DOI : 10.4171/dm/x13
Classification : 08A35, 14E30, 14J50, 37P55
Mots-clés : toric variety, Kawaguchi-Silverman conjecture, equivariant minimal model program, int-amplified endomorphism, arithmetic degree, dynamical degree 
@article{10_4171_dm_x13,
     author = {Sheng Meng and De-Qi Zhang},
     title = {Kawaguchi{\textendash}Silverman conjecture for certain surjective endomorphisms},
     journal = {Documenta mathematica},
     pages = {1605--1642},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x13},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x13/}
}
TY  - JOUR
AU  - Sheng Meng
AU  - De-Qi Zhang
TI  - Kawaguchi–Silverman conjecture for certain surjective endomorphisms
JO  - Documenta mathematica
PY  - 2022
SP  - 1605
EP  - 1642
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/x13/
DO  - 10.4171/dm/x13
ID  - 10_4171_dm_x13
ER  - 
%0 Journal Article
%A Sheng Meng
%A De-Qi Zhang
%T Kawaguchi–Silverman conjecture for certain surjective endomorphisms
%J Documenta mathematica
%D 2022
%P 1605-1642
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/x13/
%R 10.4171/dm/x13
%F 10_4171_dm_x13
Sheng Meng; De-Qi Zhang. Kawaguchi–Silverman conjecture for certain surjective endomorphisms. Documenta mathematica, Tome 27 (2022), pp. 1605-1642. doi: 10.4171/dm/x13

Cité par Sources :