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Is there a "nice" way to compute the signature of a smooth toric manifold of even complex dimension in terms of the moment polytope? By signature I mean in the sense of topology (see https://en.wikipe …

I am trying to understand the following theorem about symplectomorphisms of projective bundles. Theorem 1.5 of "Characteristic Classes in Symplectic Topology" A.G. Reznikov. Selecta Mathematica, volum …

Question: Is there a closed symplectic manifold satisfying the following? $$|Td(M)| > \sum_{i \in \mathbb{Z}} b_{i}(M) $$ here $Td(X)$ is the Todd genus of $M$ i.e. the integral of the Todd class on …

Let $M^{4}= \mathbb{P}(\mathcal{O} \oplus \mathcal{O}(1))$ and $\omega$ the symplectic form on $M^{4}$ given by the anticanonical polarisation. Suppose we form a symplectic (Gompf) sum of two copies …

From the definition of symplectic birationality given here (https://arxiv.org/pdf/0906.3265.pdf, Definition 2.1), two compact symplectic $2n$-manifolds $(M_{1},\omega_{1}),(M_{2},\omega_{2})$ are call …

I know that smooth Fano varieties over $\mathbb{C}$ may be classified into a finite number of families in each dimension (1 in dimension 1, 10 in dimension 2, 105 in dimension 3 ...). I am intereste …

What is an example of a connected symplectic manifold $(M,\omega)$, with a Hamiltonian action of $G = U(1) =S^{1}$ with infinitely many stabiliser types? Infinitely many stabiliser types means that i …

Suppose that $(M_{1},\omega_{1})$ and $(M_{2},\omega_{2})$ are compact symplectic $4$-manifolds, that are (oriented) diffeomorphic. Is it true that the Todd genus ($\frac{1}{12} (c_{1}^{2} + c_{2})(M_ …

Suppose that $A$ is a finitely generated abelian group with even rank and without $2$-torsion. Does there exist a compact symplectic $6$-manifold $(M,\omega)$ such that $A$ Is isormorphic to $H^{3}(M, …

Let $X$ be a smooth projective variety over $\mathbb{C}$. Consider the Kahler structure $(J,g,\omega)$ on $X$ induced by the Fubini-Study metric. Let $Symp(X,\omega)$ be the group of symplectomorphism …