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A complex associated to a family of ideals and applications to subspace arrangements
Abstract
We reprove and generalize a result of Derksen describing the Hilbert polynomial of the vanishing ideal of a transversal subspace arrangement in projective space. When the subspaces have all codimension 2, we describe explicitly the local cohomology modules of the corresponding defining ideal. This is achieved via a complex naturally associated to the subspace arrangement, whose basic properties are also investigated.
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BibTeX
@misc{conca2026complex,
title = {{A complex associated to a family of ideals and applications to subspace arrangements}},
author = {Aldo Conca and Manolis C. Tsakiris},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13450},
eprint = {2610.13450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13450},
}
RIS
TY - UNPB
TI - A complex associated to a family of ideals and applications to subspace arrangements
AU - Aldo Conca
AU - Manolis C. Tsakiris
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13450
UR - https://arxiv.org/abs/2610.13450
AB - We reprove and generalize a result of Derksen describing the Hilbert polynomial of the vanishing ideal of a transversal subspace arrangement in projective space. When the subspaces have all codimension 2, we describe explicitly the local cohomology modules of the corresponding defining ideal. This is achieved via a complex naturally associated to the subspace arrangement, whose basic properties are also investigated.
ER -