On a General Form of the Second Main Theorem

Ru, Min

doi:10.1090/s0002-9947-97-01913-2

Cited by 36 publications

(13 citation statements)

References 14 publications

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“…Theorem B also is improved by Min Ru [19] with a better small term. In [19], M. Ru also shows that the general form of second main theorem for fixed hyperplanes may be applied to give a simple proof for second main theorem for moving hyperplanes.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Quantitative subspace theorem and general form of second main theorem for higher degree polynomials

Quang

2018

Preprint

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This paper deals with the quantitative Schmidt's subspace theorem and the general from of the second main theorem, which are two correspondence objects in Diophantine approximation theory and Nevanlinna theory. In this paper, we give a new below bound for Chow weight of projective varieties defined over a number field. Then, we apply it to prove a quantitative version of Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety. Finally, we apply this new below bound for Chow weight to establish a general form of second main theorem in Nevanlinna theory for meromorphic mappings into projective varieties intersecting hypersurfaces in subgeneral position with a short proof. Our results improve and generalize the previous results in these directions.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Quantitative subspace theorem and general form of second main theorem for higher degree polynomials

Quang

2018

Preprint

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“…, λ D q are corresponding Weil functions, then one can define a multidivisor proximity function Definition 4.5). Second Main Theorems of this type were introduced by the second-named author [19]; see also work of the first-named author [13]. Some other applications are also given.…”

Section: Corollary 14mentioning

confidence: 99%

“…. , V , respectively, such that i=1 div(B i ) ≥ μD(13) relative to the cone of effective R-Cartier b-divisors. (iii) There are base-point-free linear subspaces…”

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confidence: 99%

An Evertse–Ferretti Nevanlinna constant and its consequences

Vojta

2021

Monatsh Math

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In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known results. This includes a 1999 example of Faltings from his Baker’s Garden article. We also extend the theory of these Nevanlinna constants to what we call “multidivisor Nevanlinna constants,” which allow the proximity function to involve the maximum of Weil functions for finitely many divisors.

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“…The following general form of the second main theorem is due to M. Ru [21] Theorem 2.6 (see [21]). Let C m → P N (C) be a linearly nondegenerate holomorphic curve with a reduced representation f = (f 0 , .…”

Section: Thenmentioning

confidence: 99%

Generalizations of degeneracy second main theorem and Schmidt's subspace theorem

Quang

2020

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In this paper, by introducing the notion of "distributive constant" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary families of hypersurfaces in projective varieties. Our second main theorem generalizes and improves previous results for meromorphic mappings with hypersurfaces, in particular for algebraically degenerate mappings and for the families of hypersurfaces in subgeneral position. The analogous results for the holomorphic curves with finite growth index from a complex disc into a project variety, and for meromorphic mappings on a complete Kähler manifold are also given. For the last aim, we will prove a Schmidt's subspace theorem for an arbitrary families of homogeneous polynomials, which is the counterpart in Number theory of our second main theorem. Our these results are generalizations and improvements of all previous results.

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On a General Form of the Second Main Theorem

Abstract: Abstract. We give a proof of a general form of the Second Main Theorem for holomorphic curves with a good error term. Two applications of this general form are also provided.

Cited by 36 publications

References 14 publications

Quantitative subspace theorem and general form of second main theorem for higher degree polynomials

Quantitative subspace theorem and general form of second main theorem for higher degree polynomials

An Evertse–Ferretti Nevanlinna constant and its consequences

Generalizations of degeneracy second main theorem and Schmidt's subspace theorem

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