# zbMATH — the first resource for mathematics

The topology of real and complex algebraic varieties. (English) Zbl 1036.14010
Maruyama, Masaki (ed.) et al., Taniguchi conference on mathematics Nara ’98. Papers from the conference, Nara, Japan, December 15–20, 1998. Tokyo: Mathematical Society of Japan (ISBN 4-931469-13-2/hbk). Adv. Stud. Pure Math. 31, 127-145 (2001).
Survey on the realization and the recognition problem. Here the “realization problem” means determining which topological spaces can be obtained as $$X(\mathbb{C})$$ or $$X(\mathbb{R})$$, where $$X$$ is an affine algebraic variety. The recognition problem asks which algebraic properties of $$X$$ are determined by topological properties of $$X(\mathbb{C})$$ or $$X(\mathbb{R})$$.
For the entire collection see [Zbl 0980.00032].

##### MSC:
 14F45 Topological properties in algebraic geometry 14P25 Topology of real algebraic varieties 14P05 Real algebraic sets 14P20 Nash functions and manifolds