Algebraic boundaries of convex semi-algebraic sets
Rainer Sinn · Research in the Mathematical Sciences · 2015
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. 2010 Mathematics Subject Classification: Primary: 52A99, 14N05, 14P10; Secondary: 51N35, 14Q15