The main purpose of this paper is to generalize the celebrated L^2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bu...The main purpose of this paper is to generalize the celebrated L^2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.展开更多
We study conditions of Hormander's L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander's L^(2)-estimate under...We study conditions of Hormander's L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander's L^(2)-estimate under some regularity assumptions on an n-dimensional domain.This result is a partial generalization of the one-dimensional result obtained by Berndtsson(1998).We also define new positivity notions for vector bundles with singular Hermitian metrics by using these conditions.We investigate these positivity notions and compare them with classical positivity notions.展开更多
基金supported by the Agence Nationale de la Recherche grant“Convergence de Gromov-Hausdorff en géeométrie khlérienne”the European Research Council project“Algebraic and Khler Geometry”(Grant No.670846)from September 2015+1 种基金the Japan Society for the Promotion of Science Grant-inAid for Young Scientists(B)(Grant No.25800051)the Japan Society for the Promotion of Science Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers
文摘The main purpose of this paper is to generalize the celebrated L^2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.
基金supported by the Program for Leading Graduate Schools,the Ministry of Education,Culture,Sports,Science and Technology,Japan,and Japan Society for the Promotion of Science,Grants-in-Aid for Scientific Research(Grant No.18J22119)。
文摘We study conditions of Hormander's L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander's L^(2)-estimate under some regularity assumptions on an n-dimensional domain.This result is a partial generalization of the one-dimensional result obtained by Berndtsson(1998).We also define new positivity notions for vector bundles with singular Hermitian metrics by using these conditions.We investigate these positivity notions and compare them with classical positivity notions.
