Uniform <i>L</i> <sup>2</sup> -estimates for flat nontrivial line bundles on compact complex manifolds
Abstract In this study, we extend the uniform <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> {L}^{2} -estimate of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mrow> <m:mo>∂</m:mo> </m:mrow> <m:mrow> <m:mo>¯</m:mo> </m:mrow> </m:mover> </m:math> \bar{\partial } -equations for flat nontrivial line bundles, proved for compact Kähler manifolds by Hashimoto and Koike, to compact complex manifolds. In the proof, by tracing the Dolbeault isomorphism in detail, we derive the desired <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> {L}^{2} -estimate directly from Ueda’s lemma.
Authors
- Takayuki Koike (ORCID: https://orcid.org/0000-0002-7860-1899)
- Shinichi Matsumura (ORCID: https://orcid.org/0000-0001-5369-4147)
- Y. Hashimoto (ORCID: https://orcid.org/0000-0001-5430-8199)
Institutions
- Tohoku University (JP)
- Osaka City University (JP)
Publication Details
- Journal
- Complex Manifolds
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1515/coma-2024-0009
- Primary Topic
- Geometry and complex manifolds
- Type
- article
- Field-Weighted Citation Impact
- 0.00