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Is every toric variety an M-variety?

Frédéric Bihan·Matthias Franz·Clint McCrory·Joost van Hamel
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Abstract

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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Frédéric Bihan, Matthias Franz, Clint McCrory, Joost van Hamel. 2005-10-11. Is every toric variety an M-variety?. https://doi.org/10.1007/s00229-006-0004-z

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