Combinatorics of compactified universal Jacobians

Lucia Caporaso; Karl Christ

doi:10.1016/j.aim.2019.02.019

Combinatorics of compactified universal Jacobians

Lucia Caporaso, Karl Christ

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We show that the combinatorial structure of the compactified universal Jacobians over M‾ _g 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.

Original language	English
Pages (from-to)	1091-1136
Number of pages	46
Journal	Advances in Mathematics
Volume	346
DOIs	https://doi.org/10.1016/j.aim.2019.02.019
State	Published - 13 Apr 2019

Keywords

Compactified Jacobian
Graph
Moduli of stable curves
Orientation

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2019.02.019

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abstract = " We show that the combinatorial structure of the compactified universal Jacobians over M‾ g 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.",

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AB - We show that the combinatorial structure of the compactified universal Jacobians over M‾ g 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.

KW - Compactified Jacobian

KW - Graph

KW - Moduli of stable curves

KW - Orientation

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Combinatorics of compactified universal Jacobians

Abstract

Keywords

ASJC Scopus subject areas

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