We show that the combinatorial structure of the compactified universal Jacobians over $Mgb$ in degrees $g-1$ and $g$ is governed by orientations on stable graphs. In particular, for a stable curve we exhibit graded stratifications of the compactified Jacobians in terms of totally cyclic, respectively rooted, orientations on its dual graph. We prove functoriality under edge-contraction of the posets of totally cyclic and rooted orientations on stable graphs.
Caporaso, L., Christ, K. (2019). Combinatorics of compactified universal Jacobians. ADVANCES IN MATHEMATICS, 346, 1091-1136 [10.1016/j.aim.2019.02.019].
Combinatorics of compactified universal Jacobians.
Lucia Caporaso
;CHRIST, KARL
2019-01-01
Abstract
We show that the combinatorial structure of the compactified universal Jacobians over $Mgb$ in degrees $g-1$ and $g$ is governed by orientations on stable graphs. In particular, for a stable curve we exhibit graded stratifications of the compactified Jacobians in terms of totally cyclic, respectively rooted, orientations on its dual graph. We prove functoriality under edge-contraction of the posets of totally cyclic and rooted orientations on stable graphs.| File | Dimensione | Formato | |
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