Abstract
In this note, we explain the additive Deligne–Simpson problem and its generalization for differential equations with unramified irregular singularities. A correspondence between spaces of solutions of these additive Deligne–Simpson problems and quiver varieties is given. As an application, the geometry of moduli spaces of meromorphic connections with unramified irregular singularities is discussed, for example, the non-emptiness of the smooth parts of moduli spaces and their connectedness. The detail of this note can also be found in [17].
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Hiroe, K. (2020). On Additive Deligne–Simpson Problems. In: Iohara, K., Malbos, P., Saito, MH., Takayama, N. (eds) Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers. Algorithms and Computation in Mathematics, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-030-26454-3_8
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