Uniform L2-estimates for flat nontrivial line bundles on compact complex manifolds

Abstract

In this study, we extend the uniform L2{L}^{2}-estimate of ∂¯\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 L2{L}^{2}-estimate directly from Ueda’s lemma.

Keywords

• ueda’s lemma
• l2-equations
• 32w05
• 53c07