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.
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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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