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- W3100019478 abstract "We prove that any symplectic Fano $6$-manifold $M$ with a Hamiltonian $S^1$-action is simply connected and satisfies $c_1 c_2(M)=24$. This is done by showing that the fixed submanifold $M_{min}subseteq M$ on which the Hamiltonian attains its minimum is diffeomorphic to either a del Pezzo surface, a $2$-sphere or a point. In the case when $dim(M_{min})=4$, we use the fact that symplectic Fano $4$-manifolds are symplectomorphic to del Pezzo surfaces. The case when $dim(M_{min})=2$ involves a study of $6$-dimensional Hamiltonian $S^1$-manifolds with $M_{min}$ diffeomorphic to a surface of positive genus. By exploiting an analogy with the algebro-geometric situation we construct in each such $6$-manifold an $S^1$-invariant symplectic hypersurface ${cal F}(M)$ playing the role of a smooth fibre of a hypothetical Mori fibration over $M_{min}$. This relies upon applying Seiberg-Witten theory to the resolution of symplectic $4$-orbifolds occurring as the reduced spaces of $M$." @default.
- W3100019478 created "2020-11-23" @default.
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- W3100019478 date "2019-01-12" @default.
- W3100019478 modified "2023-09-24" @default.
- W3100019478 title "S1‐invariant symplectic hypersurfaces in dimension 6 and the Fano condition" @default.
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- W3100019478 doi "https://doi.org/10.1112/topo.12087" @default.
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