Abstract: Multiplier ideal sheaves with line bundles have played an important role and been well-studied in complex geometry. For general vector bundles, we consider the L^2 multiplier submodule sheaf associated to a singular Hermitian metric, defined by M. A. de Cataldo. we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semipositive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Kollár-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.

Biography: Yaxiong Liu is currently a postdoc in University of Maryland. His mentor is Prof. Tamas Darvas. He obtained his PhD in Tsinghua University in Beijing under the supervision of Prof. Akito Futaki. He is interested in Kähler geometry, especially the existence of canonical Kähler metrics.

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