Details
| Original language | English |
|---|---|
| Pages (from-to) | 4605-4630 |
| Number of pages | 26 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 376 |
| Issue number | 7 |
| Early online date | 12 Apr 2023 |
| Publication status | Published - 2023 |
Abstract
We show that relative compactified Jacobians of one-parameter smoothings of a nodal curve of genus g are Mumford models of the generic fiber. Each such model is given by an admissible polytopal decomposition of the skeleton of the Jacobian. We describe the decompositions corresponding to compactified Jacobians explicitly in terms of the auxiliary stability data and find, in particular, that in degree g there is a unique compactified Jacobian encoding slope stability, and it is induced by the tropical break divisor decomposition.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 376, No. 7, 2023, p. 4605-4630.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Compactified Jacobians as Mumford models
AU - Christ, Karl
AU - Payne, Sam
AU - Shen, Tif
N1 - Funding Information: Received by the editors May 16, 2022, and, in revised form, September 2, 2022. 2020 Mathematics Subject Classification. Primary 14H40, 14T20, 14G22 . The first author was partially supported by the Israel Science Foundation (grant No. 821/16). Funding Information: The second author was partially supported by NSF DMS-1702428, NSF DMS-2001502, and NSF DMS-2053261.
PY - 2023
Y1 - 2023
N2 - We show that relative compactified Jacobians of one-parameter smoothings of a nodal curve of genus g are Mumford models of the generic fiber. Each such model is given by an admissible polytopal decomposition of the skeleton of the Jacobian. We describe the decompositions corresponding to compactified Jacobians explicitly in terms of the auxiliary stability data and find, in particular, that in degree g there is a unique compactified Jacobian encoding slope stability, and it is induced by the tropical break divisor decomposition.
AB - We show that relative compactified Jacobians of one-parameter smoothings of a nodal curve of genus g are Mumford models of the generic fiber. Each such model is given by an admissible polytopal decomposition of the skeleton of the Jacobian. We describe the decompositions corresponding to compactified Jacobians explicitly in terms of the auxiliary stability data and find, in particular, that in degree g there is a unique compactified Jacobian encoding slope stability, and it is induced by the tropical break divisor decomposition.
UR - http://www.scopus.com/inward/record.url?scp=85165582271&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1912.03653
DO - 10.48550/arXiv.1912.03653
M3 - Article
AN - SCOPUS:85165582271
VL - 376
SP - 4605
EP - 4630
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 7
ER -