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Trace ideals of syzygies
Abstract
We study the behavior of trace ideals under taking syzygies. In particular, when R is numerical semigroup ring and I is a homogeneous ideal in R, we obtain an upper estimate for trR(Ω1R(I)), and we show this estimate is sharp when I is the conductor ideal cR of R. Using this result, we characterize the numerical semigroup rings for which trR(M) ⊆ trR(Ω1R(M)) holds for every finitely generated R-module M. In a similar vein, we characterize numerical semigroup rings for which trR(Ω1R(cR))=cR.
Related
- Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings
- Trace ideals of exterior powers of the module of differentials
- Effective syzygies of secant varieties
- Syzygies of Polarized Abelian Surfaces: A Reider-Type Criterion
- A Reider-type theorem for syzygies of cyclic covers of anticanonical rational surfaces
BibTeX
@misc{lindo2026trace,
title = {{Trace ideals of syzygies}},
author = {Haydee Lindo and Justin Lyle and Sarasij Maitra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00707},
eprint = {2609.00707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00707},
}
RIS
TY - UNPB
TI - Trace ideals of syzygies
AU - Haydee Lindo
AU - Justin Lyle
AU - Sarasij Maitra
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.00707
UR - https://arxiv.org/abs/2609.00707
AB - We study the behavior of trace ideals under taking syzygies. In particular, when R is numerical semigroup ring and I is a homogeneous ideal in R, we obtain an upper estimate for tr_R(Ω^1_R(I)), and we show this estimate is sharp when I is the conductor ideal c_R of R. Using this result, we characterize the numerical semigroup rings for which tr_R(M) ⊆ tr_R(Ω^1_R(M)) holds for every finitely generated R-module M. In a similar vein, we characterize numerical semigroup rings for which tr_R(Ω^1_R(c_R))=c_R.
ER -