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Characteristic classes for algebraic vector bundles with Hermitian metric. II. (English) Zbl 0715.14006
[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 $${\mathbb{P}}^ n({\mathbb{C}})$$ [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.

##### MSC:
 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 32H30 Value distribution theory in higher dimensions 57R20 Characteristic classes and numbers in differential topology 14C35 Applications of methods of algebraic $$K$$-theory in algebraic geometry
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