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Nov 28, 2017 at 11:34 vote accept user267839
Nov 28, 2017 at 10:33 comment added Jason Starr The failure of Proposition 2 in the symplectic geometry setting is a major issue with extending much of the "minimal model program" to the symplectic setting (Ruan's program). Specifically, for an elliptic differential operator between two smooth vector bundles on the 2-sphere, as arises from the $\overline{\partial}$-equation on a holomorphic vector bundle on $\mathbb{CP}^1$, even if the kernel of the differential operator surjects onto one fiber of the domain, this does not necessarily imply vanishing of the cokernel (vanishing of $H^1$, which then implies surjectivity for every fiber).
Nov 28, 2017 at 10:33 history edited gdb CC BY-SA 3.0
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Nov 28, 2017 at 10:27 history edited gdb CC BY-SA 3.0
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Nov 28, 2017 at 6:43 history answered gdb CC BY-SA 3.0