A Schubert curve

The following is a combinatorially-defined covering space (details are in my paper):

The bottom curve is a stable curve of genus 0 with four marked points, labeled with partitions. The top curve is a solution to a Schubert problem with one degree of freedom.

The top curve is also a covering space of the curve below it! I have labeled the fibers over the bolded points, and also described bijections (called sh₂, sh₃, esh₂ and esh₃), which describe how the label changes if we follow a dashed arc or a solid arc.

We can desingularize the central curve, which corresponds to moving away from the boundary point of the moduli space M_0,4. There are two ways to do this: either the dashed lines join each other and the solid lines join each other (this gives the curve on the right), or the lines can cross (this gives the curve on the left).

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