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.

引用

页码：419 / 430

页数：12

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