Takayuki Koike

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math.CV2024

Uniform $L^{2}$ -estimates for flat nontrivial line bundles on compact complex manifolds

Yoshinori Hashimoto, Takayuki Koike, Shin-ichi Matsumura

In this paper, we extend the uniform $L^{2}$ -estimate of $\partial ˉ$ -equations for flat nontrivial line bundles, proved for compact Kähler manifolds in the previous work, to com…

math.CV2024

Cohomology groups with compact support for flat line bundles on certain complex Lie groups

Takayuki Koike, Jinichiro Tanaka

Let $X$ be a complex surface obtained as the quotient of the complex Euclidean space $C^{2}$ by a discrete subgroup of rank $3$ . We investigate the cohomology group $H_0^1(X…

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

Cohomology groups with compact support for flat line bundles on certain complex Lie groups

Uniform $L^{2}$ -estimates for flat nontrivial line bundles on compact complex manifolds