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Dear Gil, we have a nonrational construction with F. Battaglia in the case of simplicial fans here:    arXiv:1108.1637, where we use foliated compact manifolds instead of toric varieties. In this setting, Stanley's proof of (the necessary part of) the g-conjecture carries over.

Dear Gil, we have a nonrational construction in the case of simplicial fans here:  arXiv:1108.1637, where we use foliated compact manifolds instead of toric varieties. In this setting, Stanley's proof of (the necessary part of) the g-conjecture carries over.

Dear Gil, we have a nonrational construction with F. Battaglia in the case of simplicial fans here:   arXiv:1108.1637, where we use foliated compact manifolds instead of toric varieties. In this setting, Stanley's proof of (the necessary part of) the g-conjecture carries over.

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Dear Gil, we have a nonrational construction in the case of simplicial fans here: arXiv:1108.1637, where we use foliated compact manifolds instead of toric varieties. In this setting, Stanley's proof of (the necessary part of) the g-conjecture carries over.