Is every toric variety an M-variety ?

Frederic Bihan (1) , Matthias Franz (2) , Clint Mccrory (3) , Joost van Hamel (4)

1 LAMA - Laboratoire de Mathématiques
2 Department of Mathematics
3 Department of Mathematics
4 Department of mathematics, Leuven university

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.

Domaines: Géométrie algébrique [math.AG]

Frederic Bihan, Matthias Franz, Clint Mccrory, Joost van Hamel. Is every toric variety an M-variety ?. Manuscripta mathematica, 2006, 120, pp.217-232. ⟨hal-00386973⟩