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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)
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957: [] 2023/07/31(月) 09:17:00.22 ID:jznoxopE 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. http://rio2016.5ch.net/test/read.cgi/math/1674527723/957
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