Abstract
We obtain an optimal \(L^2\) extension theorem for a certain class of holomorphic sections of a Hermitian holomorphic line bundle from a possibly non-reduced subvariety in a Stein manifold, which optimized Demailly’s \(L^2\) extension theorem from non-reduced subvarieties in the case of Stein manifolds. As applications, we obtain an optimal \(L^2\) extension theorem concerning a certain class of jets and a sufficient and necessary condition under which a generalized Bergman kernel attains its sharp lower bound.
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In memory of Professor Jean-Pierre Demailly.
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This research is supported by National Key R &D Program of China (2021YFA1002600 and 2021YFA1003100). Z. Li and X. Zhou are supported by the NSFC Grant (No. 12201060) and (No. 12288201) respectively.
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Li, Z., Xu, W. & Zhou, X. On Demailly’s \(L^2\) extension theorem from non-reduced subvarieties. Math. Z. 305, 23 (2023). https://doi.org/10.1007/s00209-023-03351-1
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DOI: https://doi.org/10.1007/s00209-023-03351-1