General form of second main theorem on generalized $p$-Parabolic manifolds for arbitrary closed subschemes

TL;DR

This paper extends the second main theorem to generalized p-Parabolic manifolds, providing a broad framework for meromorphic mappings intersecting arbitrary subschemes with explicit truncation levels.

Contribution

It introduces the distributive constant for families of closed subschemes and establishes a general second main theorem in this context.

Findings

Established a general second main theorem for meromorphic mappings on p-Parabolic manifolds.

Derived explicit truncation levels for counting functions in intersection problems.

Extended classical results to arbitrary families of closed subschemes.

Abstract

By introducing the notion of distributive constant for a family of closed subschemes, we establish a general form of the second main theorem for algebraic nondegenerate meromorphic mappings from a generalized $p$-Parabolic manifold into a projective variety with arbitrary families of closed subschemes. As its consequence, we give a second main theorem for such meromorphic mappings intersecting arbitrary hypersurfaces with an explicitly truncation level for the counting functions.