an:04177246
Zbl 0715.14006
Gillet, Henri; Soul??, Christophe
Characteristic classes for algebraic vector bundles with Hermitian metric. II
EN
Ann. Math. (2) 131, No. 2, 205-238 (1990).
00283972
1990
j
14F05 32H30 57R20 14C35
Nevanlinna theory for maps into complex projective n-space; arithmetic Chern classes; Beilinson regulator on \(K_ 1\)
[For part I of this paper see ibid., No.1, 163-203 (1990; Zbl 0715.14018).]
This part II has three sections. In section 5, the case \(X={\mathbb{P}}^ n\) (the projective space) is considered; one computes the arithmetic Chern classes of the canonical rank \(n\) vector bundle on X, which are given by the \(L^ 1\quad forms\) introduced by Levine in his paper on Nevanlinna theory for maps into \({\mathbb{P}}^ n({\mathbb{C}})\) [\textit{H. I. Levine}, Ann. Math., II. Ser. 71, 529-535 (1960; Zbl 0142.048)]. In section 6, one introduces \(\hat K_ 0(X)\) and one describes it by some exact sequences. In the last section, one gives a new description of the Beilinson regulator on \(K_ 1\)(X) by means of Bott-Chern forms, and one shows that ch is an isomorphism of \(\lambda\)-rings.
Vasile Br??nz??nescu
Zbl 0715.14018; Zbl 0142.048