Abstract

Let X be a compact Kähler manifold of dimension n. Let A and B be two analytic submanifolds of dimensions p and q respectivelly. Assume p + q = n - 1, A and B intersect cleanly at a submanifold M of dimension m. Let At be a differentiable deformation of A = A0 for the complex number t around 0, such that AtB = Ø for t ≠ 0, and the deformation At is analytic in a neighborhood of M. Let GB be a Green's current of B (smooth on X\B). We prove the asymptotic formula ∫At GB = e log |t|2 + O(1) where e = ∫Mcm(TX/(TA + TB)). The asymptotics suggest that e is an obstruction to the existence of positive Green's currents.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 229-249
Launched on MUSE
1998-04-01
Open Access
No
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