The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of the American Mathematical Society
( Vol. 10 NO.1 / (1997))
Uniformly of rational points
Lucia Caporaso, Joe Harris, Barry Mazur,
Pages. 1-35
Abstract
Contents 1. Uniformity and correlation
1.1 Introduction
1.2 Proof of the uniform bound theorem
1.3 Proof of the universal generic bound theorem
1.4 The correlation theorem
2. Examples
2.1 Pencils of plane quartics
2.2 An isotrivial family
2.3 Adjoint conditions and canonical singularities
2.4 Proof of correlation for isotrivial families
3. Families with maximal variation of moduli
3.1 Preliminaries
3.2 Proof of correlation for families with maximal variation
4. Families of stable curves with group action
4.1 Statement of the main proposition
4.2 Singularities of quotients: adjoint conditions
4.3 Proof of the main proposition and other corollaries
5. The general case
5.1 Stable reduction over arbitrary bases
5.2 Completion of the proof of the correlation theorem 1.3
6. The higher-dimensional case
6.1 Correlation for families of higher-dimensional varieties
6.2 Geometric consequences of the higher-dimensional conjecture
6.3 An arithmetic consequence of the higher-dimensional conjecture
Key words
Mathmatical Subject Classification 14G05, 14H10