Hodge metrics and the curvature of higher direct images

Christophe Mourougane; Shigeharu Takayama

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 6, page 905-924
  • ISSN: 0012-9593

Abstract

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Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.

How to cite

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Mourougane, Christophe, and Takayama, Shigeharu. "Hodge metrics and the curvature of higher direct images." Annales scientifiques de l'École Normale Supérieure 41.6 (2008): 905-924. <http://eudml.org/doc/272191>.

@article{Mourougane2008,
abstract = {Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.},
author = {Mourougane, Christophe, Takayama, Shigeharu},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {higher direct images; Hodge metrics; harmonic theory for relative cohomology; Nakano positivity},
language = {eng},
number = {6},
pages = {905-924},
publisher = {Société mathématique de France},
title = {Hodge metrics and the curvature of higher direct images},
url = {http://eudml.org/doc/272191},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Mourougane, Christophe
AU - Takayama, Shigeharu
TI - Hodge metrics and the curvature of higher direct images
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 6
SP - 905
EP - 924
AB - Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.
LA - eng
KW - higher direct images; Hodge metrics; harmonic theory for relative cohomology; Nakano positivity
UR - http://eudml.org/doc/272191
ER -

References

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