Heights of projective varieties and positive Green forms

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

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