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Asymptotics of Partial Density Functions for Divisors

Ross, J; Singer, M; (2017) Asymptotics of Partial Density Functions for Divisors. Journal of Geometric Analysis , 27 (3) pp. 1803-1854. 10.1007/s12220-016-9741-8. Green open access

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Abstract

We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor Y. Assuming the data in question is invariant under an (Formula presented.)-action (locally around Y) we prove that this density function has a distributional asymptotic expansion that is in fact smooth upon passing to a suitable real blow-up. Moreover we recover the existence of the “forbidden region” R on which the density function is exponentially small, and prove that it has an “error-function” behaviour across the boundary (Formula presented.). As an illustrative application, we use this to study a certain natural function that can be associated to a divisor in a Kähler manifold.

Type: Article
Title: Asymptotics of Partial Density Functions for Divisors
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s12220-016-9741-8
Publisher version: http://doi.org/10.1007/s12220-016-9741-8
Language: English
Additional information: Copyright © The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Interface asymptotics, Forbidden region, Equilibrium set, Bergman kernel
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1522156
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