A lower bound for the degree of certain plane curves with prescribed singularities.

被引：7
|
作者：
Evain, L [1 ]
机构：
[1] Univ Angers, Dept Math, F-49045 Angers, France
来源：
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE | 1998年 / 126卷 / 04期
关键词：
D O I：
10.24033/bsmf.2335
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that the degree of a projective plane curve through r generic points with multiplicity m is strictly greater than root rm provided one of the following two conditions is satisfied r is a perfect square greater or equal to ten or r is greater than (8m(m + 1)/(4m - 1))(2) This result is part of a conjecture of Nagata, and the first case was already known to Nagata himself.
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页码：525 / 543
页数：19
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