Real toric varieties #2055
MVallee1998
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Hi @MVallee1998, just to clarify: are you proposing to work on this? Or are you requesting that someone else should work on it? |
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Dear developers,
The current work on this Julia package is auspicious and has picked my interest.$X(\Sigma)$ , one can associate a real toric variety $X^{\mathbb{R}}(\Sigma^{\mathbb{R}})$ which is its real locus and whose fan $\Sigma^{\mathbb{R}}$ is the mod 2 reduction of $\Sigma$ .$X^{\mathbb{R}}$ can be computed from the mod 2 fan and is a quotient ring in $\mathbb{Z}/2\mathbb{Z}$ by some ideal coming from the mod 2 fan. An explicit example is computed by hand here.$\mathbb{Z}/4\mathbb{Z}$ -homology can also be computed easily from the mod 2 fan and the simplicial $\mathbb{Z}/2\mathbb{Z}$ -homology of the simplicial complex underlying the mod 2 fan, the formula is provided here.$\Sigma^{\mathbb{R}}$ , can we find a complete nonsingular (integral) fan $\Sigma$ , called a lift, whose mod 2 reduction is $\Sigma^{\mathbb{R}}$ ?
I want to suggest some new functionalities.
To any complex toric variety
Just as in the complex case, the cohomology of
The
Finally, there is a big question in toric topology called the 'lifting conjecture': given a complete nonsingular mod 2 fan
No efficient algorithm for finding such a lift exist.
Best regards,
Mathieu Vallée
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