A Note on the Complexity of Real Algebraic Hypersurfaces

被引：0
|
作者：
Kerber, Michael [1 ]
Sagraloff, Michael [2 ]
机构：
[1] IST Inst Sci & Technol Austria, A-3400 Klosterneuburg, Austria
[2] Max Planck Inst Informat, D-66123 Saarbrucken, Germany
来源：
GRAPHS AND COMBINATORICS | 2011年 / 27卷 / 03期
关键词：
Algebraic curves; Algebraic surfaces; Triangulation; Isotopy; TRIANGULATIONS;
D O I：
10.1007/s00373-011-1020-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given an algebraic hypersurface O in R(d) , how many simplices are necessary for a simplicial complex isotopic to O ? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d a parts per thousand yen 3.
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页码：419 / 430
页数：12
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