Please use this identifier to cite or link to this item: `https://scholarbank.nus.edu.sg/handle/10635/234652`
 Title: Kawaguchi-Silverman conjecture for surjective endomorphisms Authors: Meng, Sheng Zhang, De-Qi Keywords: math.AGmath.AGmath.DSmath.NT37P55, 14E30, 08A35 Issue Date: 5-Aug-2019 Citation: Meng, Sheng, Zhang, De-Qi (2019-08-05). Kawaguchi-Silverman conjecture for surjective endomorphisms. ScholarBank@NUS Repository. Abstract: 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 \$\mathbb{Q}\$-factorial Kawamata log terminal projective variety admitting an 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 an 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. URI: https://scholarbank.nus.edu.sg/handle/10635/234652 Appears in Collections: Staff PublicationsElements

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