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### Software for computing multi-graded Hilbert series

The ring of invariants $S^T$ of $k[a,b,c,d]$ under the algebraic torus action $T = k^{*}$ with weights (1,1,-1,-1)
is $S = k[ac,ad,bc,bd]$ which has multigraded Hilbert series
$\frac{1 - ...

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### Moment map for toric actions — online references?

Consider a toric variety, defined as a (normal?) complex projective variety $X$ together with an algebraic action of $(\mathbb C^*)^n$ with finitely many orbits. Now we have two "real symplectic" ...

**8**

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### Hamiltonian S^1 actions with isolated fixed points

I have in mind the following question for some time. Is there an example of a compact symplectic manifold with a Hamiltonian S^1 action with isolated fixed points, that does not admit a compatible S^1 ...