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Asymptotic expansions of L2-extension indices and curvature positivity

  • Takahiro Inayama
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Abstract

In this paper, we prove an asymptotic expansion of the L2-extension index of a smooth Hermitian metric on a holomorphic vector bundle, in which the Chern curvature appears as the second-order coefficient. By using this expansion, we show in a unified way that there is an equivalence between how sharp the L2-extension is and how positive or negative the curvature is. We also introduce a new notion of q-L2-extension indices and investigate partial positivity and flatness in terms of these indices.

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Cite

BibTeXRIS
BibTeX
@misc{inayama2026asymptotic,
  title = {{Asymptotic expansions of $L^2$-extension indices and curvature positivity}},
  author = {Takahiro Inayama},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15088},
  eprint = {2609.15088},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15088},
}
RIS
TY  - UNPB
TI  - Asymptotic expansions of L^2-extension indices and curvature positivity
AU  - Takahiro Inayama
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15088
UR  - https://arxiv.org/abs/2609.15088
AB  - In this paper, we prove an asymptotic expansion of the L^2-extension index of a smooth Hermitian metric on a holomorphic vector bundle, in which the Chern curvature appears as the second-order coefficient. By using this expansion, we show in a unified way that there is an equivalence between how sharp the L^2-extension is and how positive or negative the curvature is. We also introduce a new notion of q-L^2-extension indices and investigate partial positivity and flatness in terms of these indices.
ER  -