Is every toric variety an M-variety?

Details Is every toric variety an M-variety? Is every toric variety an M-variety?

2005-10-11

arxiv.org/abs/math/0510228v1

Manuscripta Math. 120 (2006), 217-232

Mathematics

Algebraic Geometry

13 pages

Scientific paper

10.1007/s00229-006-0004-z

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.

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