Asymptotics of eigensections on toric varieties

A. Huckleberry[1]; H. Sebert[1]

  • [1] Fakulät und Institut für Mathematik Ruhr Universität Bochum Universitätsstrasse 150 D-44780 Bochum, Germany

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 2, page 733-762
  • ISSN: 0373-0956

Abstract

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Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities | ϕ n | 2 = | s N | 2 / | | s N | | L 2 2 for eigensections s N ∈ Γ ( X , L N ) approaching a semiclassical ray. Here X is a normal compact toric variety and L is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch.

How to cite

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Huckleberry, A., and Sebert, H.. "Asymptotics of eigensections on toric varieties." Annales de l’institut Fourier 63.2 (2013): 733-762. <http://eudml.org/doc/275464>.

@article{Huckleberry2013,
abstract = {Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities $| \varphi _n| ^2=| s_N| ^2 / || s_N||_\{L^2\}^2$ for eigensections $s_N\in \Gamma (X,L^N)$ approaching a semiclassical ray. Here $X$ is a normal compact toric variety and $L$ is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch.},
affiliation = {Fakulät und Institut für Mathematik Ruhr Universität Bochum Universitätsstrasse 150 D-44780 Bochum, Germany; Fakulät und Institut für Mathematik Ruhr Universität Bochum Universitätsstrasse 150 D-44780 Bochum, Germany; Institut Elie Cartan UMR 7502 Université de Lorraine, CNRS, INRIA et Universitaire de France, BP 239-F-54566, Vandoeuvre-lès-Nancy Cedex.France},
author = {Huckleberry, A., Sebert, H.},
journal = {Annales de l’institut Fourier},
keywords = {asymptotics of eigensections; toric varieties; plurisubharmonic; plurisubharmonic function},
language = {eng},
number = {2},
pages = {733-762},
publisher = {Association des Annales de l’institut Fourier},
title = {Asymptotics of eigensections on toric varieties},
url = {http://eudml.org/doc/275464},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Huckleberry, A.
AU - Sebert, H.
TI - Asymptotics of eigensections on toric varieties
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 2
SP - 733
EP - 762
AB - Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities $| \varphi _n| ^2=| s_N| ^2 / || s_N||_{L^2}^2$ for eigensections $s_N\in \Gamma (X,L^N)$ approaching a semiclassical ray. Here $X$ is a normal compact toric variety and $L$ is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch.
LA - eng
KW - asymptotics of eigensections; toric varieties; plurisubharmonic; plurisubharmonic function
UR - http://eudml.org/doc/275464
ER -

References

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  12. H. Sebert, Semiclassical limits of Kählerian potentials on toric varieties 
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