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Addendum to "Defects for ample divisors of abelian varieties, Schwarz Lemma, and hyperbolic hypersurfaces of low degrees," (vol 119, pg 1139, 1997)
被引:12
|作者:
Siu, YT
[1
]
Yeung, SK
机构:
[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
关键词:
D O I:
10.1353/ajm.2003.0020
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
This addendum uses Bloch's original technique of ordinary differential equations to circumvent a difficulty in the proof of Lemma 2 in the paper in the title. This technique at the same time yields the following stronger Nevanlinna's Second Main Theorem with truncation at an order given explicitly by the Chem class of the divisor. For an ample divisor D in an abelian variety A of complex dimension n and for any holomorphic map f: C --> A whose image is not contained in any translate of D, the characteristic function of f for D is dominated by the counting function of f for D truncated at order k(n) plus an error term of logarithmic order of the characteristic function, where k(n) is inductively given by k(0) = 0, k(1) = 1, and k(l+1) = k(l) + 3(n-l-1)(4(k(l) + 1))D-l(n) for 1 less than or equal to l < n.
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页码:441 / 448
页数:8
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