Heights of projective varieties and positive Green forms
Heights of projective varieties and positive Green forms
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DOI：
10.1090/s0894-0347-1994-1260106-x
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发表时间：
1994-01
影响因子：
3.9
通讯作者：
J. Bost;H. Gillet;C. Soulé
中科院分区：
文献类型：
--
作者：
J. Bost;H. Gillet;C. Soulé
利用算术交理论，建立了代数整数环上投射簇的高度理论。这些高度是对韦尔、施密特、涅斯捷连科、菲利蓬和法尔廷斯所考虑的高度的概括。证明了它们的一些性质，包括下界和算术Bezout定理的两个投影品种的交集的高度。新的估计（广义）结果的大小。文中所用的分析工具是解析子簇的"绿色形式"，并讨论了正绿色形式的存在性.（J. - B. Bost和C. Institut des HAUTES ETUDES SCIENTIFIQUES，35，ROUTE DE CHARTRES，91440，BURES-SUR-Yvettes，FRANCE（H.数学、统计学和计算机科学系，（M/c249），伊利诺伊大学芝加哥分校，851 S。摩根街，芝加哥，伊利诺伊州60607电子邮件地址：henriGmath。国际刑事法院联合会。edu许可证或版权限制可能适用于重新分发;请参阅www.example.com
Using arithmetic intersection theory, a theory of heights for projective varieties over rings of algebraic integers is developed. These heights are generalizations of those considered by Weil, Schmidt, Nesterenko, Philippon, and Faltings. Several of their properties are proved, including lower bounds and an arithmetic Bezout theorem for the height of the intersection of two projective varieties. New estimates for the size of (generalized) resultants are derived. Among the analytic tools used in the paper are "Green forms" for analytic subvarieties, and the existence of poSitive Green forms is discussed. (J.-B.Bost and C. Soule) INSTITUT DES HAUTES ETUDES ScIENTIFIQUES,35,RoUTE DE CHARTRES, 91440, BURES-SUR-YvETTES, FRANCE (H. Gillet) DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE, (M/c249), UNIVERSITY OF ILLINOIS AT CHICAGO, 851 S. MORGAN STREET, CHICAGO, ILLINOIS 60607 E-mail address: henriGmath. uic . edu License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use