L^2 extension of adjoint line bundle sections

Abstract

We prove an L 2 extension theorem of Ohsawa-Takegoshi type for extending holomorphic sections of line bundles from a subvariety which is given as a maximal log-canonical center of a pair and is of general codimension in a projective variety. Our method of proof indicates that such a setting is the most natural one in a sense, for general L 2 extension of line bundle sections.Acknowledgement. This is a version of a Ph.D. thesis at Princeton University in 2007. I am very grateful to my advisor Professor János Kollár for his generous encouragement and sup-

Quantitative extensions of pluricanonical forms and closed positive currents

“…This result is not a consequence of theorem 0.1, but of its proof: the only difference is the version of the Ohsawa-Takegoshi theorem to be used in the inductive process. Moreover, following [27] it is possible to formulate (and prove) the higher codimensional analogue of the previous statement -where the hypersurface S will be replaced by a maximal center of some Q-divisor.…”

“…If p = q = 1, then this is precisely the Ohsawa-Takegoshi extension theorem recalled above. For p ≥ 2 the origins of the qualitative part of our result is the work of Siu see [40], [41], and also [10], [14], [16], [17], [18], [19], [20], [21], [25], [26], [27], [29], [30], [35], [44], [45], [46], [47], [49] for related statements.…”

“…Under these circumstances, the extension theorem established in [32] (and subsequently developed in [1], [2], [13], [27], [33], [34], [41], [46]) states as follows: let u be a holomorphic section of the bundle K X + L |X 0 which is L 2 with respect to h L , i.e.…”

Restricted Bergman kernel asymptotics

“…Theorem 1.4 can be derived from Theorem 4 of [Ohs01] by a standard approximation technique. See also [Kim10]. It seems most likely that a slight change of the proof of Theorem 4.2 of [Kim10] can yield Theorem 1.4.…”

“…See also [Kim10]. It seems most likely that a slight change of the proof of Theorem 4.2 of [Kim10] can yield Theorem 1.4. At any rate we give a self-contained proof in Section 5, as a courtesy to the reader.…”