Triangulation of Locally Semi-Algebraic Spaces.

Triangulation;Algebraic Geometry;Algebraic Topology;Algebraic Varieties;Mathematics;Science;Mathematics

Hofmann, Kyle RogerTappenden, James P. ;

University of Michigan

关键词: Triangulation;    Algebraic Geometry;    Algebraic Topology;    Algebraic Varieties;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/63851/krhofman_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We give necessary and sufficient conditions for a locally semi-algebraic space to be homeomorphic to a simplicial complex. Our proof does not require the space to be embedded anywhere, and it requires neither compactness nor projectivity of the space. A corollary is that every real or complex algebraic variety is triangulable, a result which does not seem to be available in the literature when the variety is neither projective nor real and compact.