[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）13 (1002ﾚｽ)
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957: 2023/07/31(月)09:17 ID:jznoxopE(7/50) AAS
More precisely, the proof is an application of the finite-dimensionality
of L^2 ¯∂-cohomology groups on M with coefficients in line bundles whose
curvature form is positive at infinity. Recall that the idea of exploiting
the finite-dimensionality for producing holomorphic sections originates
in a celebrated paper [G] of Grauert. Shortly speaking, it amounts to
finding infinitely many linearly independent C^∞ sections s1, s2, . . . of
the bundle in such a way that some nontrivial linear combination of
¯∂s1,
¯∂s2, . . . , say ?^N_{k=1} c_k¯∂sk(ck ∈ C), is equal to ¯∂u for some u which
is more regular than ?^N_{k=1} cksk.

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