A generalized Schmidt's subspace theorem for algebraic points of bounded degree

Abstract

Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has already been richly developed. Building upon this framework, we establish a Schmidt subspace theorem for algebraic points of bounded degree with respect to numerically equivalent ample divisors, attaining the optimal factor known to date and deriving a generalized weighted version. Also, we settle a longstanding open conjecture in this field.

25 pages, added a conjecture part, comments are welcome!