# All Questions

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### Cohomology of Homogeneous Complex Manifolds

Let $M$ be compact $G$-homogeneous manifold, equipped with the equivariant complex structure, when $G$ is a semi-simple algebraic group. The obvious example is every flag manifold. In that case, all ...
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### Is there any topological information encoded by the zero locus of a complex Hessian?

On a Kahler manifold one can always find a function $K$ so that (up to some constant) the Kahler form $\omega$ can be written as $\omega = \partial \bar{\partial}K$ (sometimes, under conditions that I ...
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### Fiber Bundle with a perfect bilinear map

Let $\pi:X\rightarrow Y$ a double cover of Riemann surfaces, and consider a $SL_n-$bundle $E$ with a perfect $\mathcal O_Y-$bilinear pairing $$\psi:\pi_*E\times\pi_*E\rightarrow\pi_*\mathcal O_X$$ ...
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### Finitely generated ordered monoids and noetherian subsets

(This question was asked a long time ago on MSE but got no answer so far...) Let $E$ be an additively written cancellable commutative monoid with no non-trivial units. We furnish $E$ with the order ...
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### How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, … algebras?

There is a theorem (I believe by Ocneanu) that the Markov trace on the tower of Temperley-Lieb algebras is (essentially) unique. What about just traces on separate algebras? That is, take one of ...
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### Analytic equivalence relations whose classes are sometimes Borel

There are analytic equivalence relations for which the statement "All classes are Borel" is independent of $ZFC$. In all the examples I know about, the classes are non Borel in $L$ or $L[z]$ for some ...
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### If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general? [on hold]

(Note: This has been cross-posted to MSE. However, I feel that it is more likely to receive a good answer here, because I believe that it is a research-level question. For the mathematicians who ...
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