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A generalized Poincare-Lelong formula

Mats Andersson (Institutionen för matematiska vetenskaper)
Mathematica Scandinavica (0025-5521). Vol. 101 (2007), 2, p. 195-218.
[Artikel, refereegranskad vetenskaplig]

We prove a generalization of the classical Poincare-Lelong formula. Given a holomorphic section f, with zero set Z, of a Hermitian vector bundle E -> X, let S be the line bundle over X\Z spanned by f and let Q = E/S. Then the Chern form c(D-Q) is locally integrable and closed in X and there is a current W such that dd(c)W = c(D-E) - c(D-Q) - M, where M is a current with support on Z. In particular, the top Bott-Chern class is represented by a current with support on Z. We discuss positivity of these currents, and we also reveal a close relation with principal value and residue currents of Cauchy-Fantappie-Leray type.


Denna post skapades 2008-12-15. Senast ändrad 2016-01-12.
CPL Pubid: 81397


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