Height Bounds and Preperiodic Points for Families of Jointly Regular Affine Maps

Silverman, Joseph H.

doi:10.4310/pamq.2006.v2.n1.a5

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…This result is a generalization of [14,Section 4]. The proof is almost the same except one: the only difference is that we have an improved height inequality for a jointly regular family.…”

Section: An Application To Arithmetic Dynamicsmentioning

confidence: 78%

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Height Bound and Preperiodic Points for Jointly Regular Families of Rational Maps

Lee¹

2011

Journal of the Korean Mathematical Society

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“…This result is a generalization of [14,Section 4]. The proof is almost the same except one: the only difference is that we have an improved height inequality for a jointly regular family.…”

Section: An Application To Arithmetic Dynamicsmentioning

confidence: 78%

“…Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : P n Q → R be the logarithmic absolute height on the projective space, let r(f ) be the…”

mentioning

confidence: 99%

Height Bound and Preperiodic Points for Jointly Regular Families of Rational Maps

Lee¹

2011

Journal of the Korean Mathematical Society

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“…This conjecture was verified for affine plane automorphisms by Denis [Den95], for regular automorphisms and for triangular automorphisms by Marcello [Mar00,Mar03]. See also [Lee11,Lee18,Sil06] for some variants.…”

Section: Introductionmentioning

confidence: 88%

Periodic points and arithmetic degrees of certain rational self-maps

Wang¹

2022

Preprint

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Consider a cohomologically hyperbolic birational self-map defined over the algebraic numbers, for example, a birational self-map in dimension two with the first dynamical degree greater than one, or in dimension three with the first and the second dynamical degrees distinct. We give a boundedness result about heights of its periodic points. This is motivated by a conjecture of Silverman for affine automorphisms. We also study the Kawaguchi-Silverman conjecture concerning the dynamical and the arithmetic degrees for birational self-maps in dimension two. In particular, we reduce the problem to the dynamical Mordell-Lang conjecture and verify the Kawaguchi-Silverman conjecture for some new cases.

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Quivers, invariants and quotient correspondence

Kim

2013

Journal of Algebra

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Abstract. This paper studies the geometric and algebraic aspects of the moduli spaces of quivers of fence type. We first provide two quotient presentations of the quiver varieties and interpret their equivalence as a generalized Gelfand-MacPherson correspondence. Next, we introduce parabolic quivers and extend the above from the actions of reductive groups to the actions of parabolic subgroups. Interestingly, the above geometry finds its natural counterparts in the representation theory as the branching rules and transfer principle in the context of the reciprocity algebra. The last half of the paper establishes this connection.

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Height Bounds and Preperiodic Points for Families of Jointly Regular Affine Maps

Cited by 5 publications

References 9 publications

Height Bound and Preperiodic Points for Jointly Regular Families of Rational Maps

Height Bound and Preperiodic Points for Jointly Regular Families of Rational Maps

Periodic points and arithmetic degrees of certain rational self-maps

Quivers, invariants and quotient correspondence

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