Algebraic boundaries of convex semi-algebraic sets

被引：15
|
作者：
Sinn, Rainer [1 ]
机构：
[1] Georgia Inst Technol, Sch Math, 686 Cherry St NW, Atlanta, GA 30332 USA
来源：
RESEARCH IN THE MATHEMATICAL SCIENCES | 2015年 / 2卷 / 01期
关键词：
Algebraic boundary; Convex semi-algebraic set; Projective dual variety;
D O I：
10.1186/s40687-015-0022-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of facets of a polytope with the vertices of the dual polytope to general semi-algebraic convex sets. In this case, exceptional families of extreme points might exist and we characterise them semi-algebraically. We also give a strategy for computing a complete list of exceptional families, given the algebraic boundary of the dual convex set.
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页数：18
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