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Since the great work on holomorphic curves into algebraic varietiesintersecting hypersurfaces in general position established by Ru in 2009,recently there has been some developments on the second main theorem intoalgebraic varieties intersecting moving hypersurfaces targets. The main purposeof this paper is to give some interesting improvements of Ru's second maintheorem for moving hypersurfaces targets located in subgeneral position withindex.

Second main theorem for holomorphic curves into algebraic varieties intersecting moving hypersurfaces targets