the second main theorem
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2020 ◽  
Vol 31 (06) ◽  
pp. 2050045
Author(s):  
Si Duc Quang

In this paper, we establish a new second main theorem for meromorphic mappings of [Formula: see text] into [Formula: see text] and moving hypersurfaces with truncated counting functions in the case, where the meromorphic mappings may be algebraically degenerate. A version of the second main theorem with weighted counting functions is also given. Our results improve the recent results on this topic. As an application, an algebraic dependence theorem for meromorphic mappings sharing moving hypersurfaces is given.



2020 ◽  
Vol 31 (06) ◽  
pp. 2050042
Author(s):  
Lei Shi

In this paper, under the refinement of the subgeneral position, we give an improvement for the Second Main Theorem with truncated counting functions of algebraically non-degenerate holomorphic curves into algebraic varieties [Formula: see text] intersecting divisors in subgeneral position with some index.



2019 ◽  
Vol 377 (1-2) ◽  
pp. 759-795 ◽  
Author(s):  
Min Ru ◽  
Nessim Sibony


2018 ◽  
Vol 11 (04) ◽  
pp. 1850053
Author(s):  
Pham Duc Thoan

In this paper, we show some Second Main Theorems for zero-order meromorphic mappings intersecting slowly moving targets in [Formula: see text] by considering their [Formula: see text]-Casorati determinant. Our results are [Formula: see text]-difference analogues of Cartan’s Second Main Theorem for moving targets. As an application, we give an unicity theorem for meromorphic mappings of [Formula: see text] into [Formula: see text] under the growth condition “order [Formula: see text]”.





2017 ◽  
Vol 82 (4) ◽  
pp. 1317-1355
Author(s):  
PHILIPP SCHLICHT

AbstractWe extend Solovay’s theorem about definable subsets of the Baire space to the generalized Baire spaceλλ, whereλis an uncountable cardinal withλ<λ= λ. In the first main theorem, we show that the perfect set property for all subsets ofλλthat are definable from elements ofλOrd is consistent relative to the existence of an inaccessible cardinal aboveλ. In the second main theorem, we introduce a Banach–Mazur type game of lengthλand show that the determinacy of this game, for all subsets ofλλthat are definable from elements ofλOrd as winning conditions, is consistent relative to the existence of an inaccessible cardinal aboveλ. We further obtain some related results about definable functions onλλand consequences of resurrection axioms for definable subsets ofλλ.



Author(s):  
Marian B. Pour-El ◽  
J. Ian Richards




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