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Height estimates for rational maps.

Lee, ChongGyu (Joey).

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Height estimates for rational maps.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Height estimates for rational maps./
Author:	Lee, ChongGyu (Joey).
Description:	72 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-11, Section: B, page: 6808.
Contained By:	Dissertation Abstracts International71-11B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3430193
ISBN:	9781124302089

Height estimates for rational maps.
Lee, ChongGyu (Joey).

Height estimates for rational maps. - 72 p.

Source: Dissertation Abstracts International, Volume: 71-11, Section: B, page: 6808.

Thesis (Ph.D.)--Brown University, 2010.

There is a good inequality between the height of a point and the height of the image of the point by given morphism. When we have a rational map, then it is invalid because the functorial property fails. However, we can find a weaker inequality by introducing a new invariant of a rational map, the D-ratio. By observing the geometric definition of the degree of a morphism, we define the D-ratio of a rational map. The D-ratio of a rational map will serve an important role in height inequalities for a rational map as the degree does for a morphism. In Chapter 2, the author gives preliminaries including the resolution of indeterminacy. In Chapter 3, the author defines An -effectiveness of divisors, which is essential in defining the main concept of the dissertation, and the D-ratio, the main idea of this work. We give some applications to height inequalities in Chapter 4 and to arithmetic dynamics in Chapter 5. We have a detailed example of a regular affine automorphism in Chapter 6. Finally, the author introduces further questions and future work in Chapter 7.

ISBN: 9781124302089Subjects--Topical Terms:

1669109
Applied Mathematics.

Height estimates for rational maps.
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020 $a 9781124302089
035 $a (UMI)AAI3430193
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100 1 $a Lee, ChongGyu (Joey). $3 1675424
245 1 0 $a Height estimates for rational maps.
300 $a 72 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-11, Section: B, page: 6808.
500 $a Adviser: Joseph H. Silverman.
502 $a Thesis (Ph.D.)--Brown University, 2010.
520 $a There is a good inequality between the height of a point and the height of the image of the point by given morphism. When we have a rational map, then it is invalid because the functorial property fails. However, we can find a weaker inequality by introducing a new invariant of a rational map, the D-ratio. By observing the geometric definition of the degree of a morphism, we define the D-ratio of a rational map. The D-ratio of a rational map will serve an important role in height inequalities for a rational map as the degree does for a morphism. In Chapter 2, the author gives preliminaries including the resolution of indeterminacy. In Chapter 3, the author defines An -effectiveness of divisors, which is essential in defining the main concept of the dissertation, and the D-ratio, the main idea of this work. We give some applications to height inequalities in Chapter 4 and to arithmetic dynamics in Chapter 5. We have a detailed example of a regular affine automorphism in Chapter 6. Finally, the author introduces further questions and future work in Chapter 7.
590 $a School code: 0024.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
690 $a 0364
690 $a 0405
710 2 $a Brown University. $3 766761
773 0 $t Dissertation Abstracts International $g 71-11B.
790 1 0 $a Silverman, Joseph H., $e advisor
790 $a 0024
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3430193