@article{a0cf2449b3be4dff87c694745c397f49,
title = "Betti numbers of symmetric shifted ideals",
abstract = "We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetric shifted ideal has linear quotients and compute its (equivariant) graded Betti numbers. As an application of this result, we obtain several consequences for graded Betti numbers of symbolic powers of defining ideals of star configurations.",
keywords = "Betti numbers, Equivariant resolution, Linear quotients, Shifted ideal, Star configuration, Symbolic power",
author = "Jennifer Biermann and {de Alba}, Hern{\'a}n and Federico Galetto and Satoshi Murai and Uwe Nagel and Augustine O'Keefe and Tim R{\"o}mer and Alexandra Seceleanu",
note = "Funding Information: The research of the fourth author is partially supported by KAKENHI 16K05102 . The fifth author was partially supported by Simons Foundation grant # 317096 . The last author was supported by NSF grant DMS–1601024 and EPSCoR award OIA–1557417 . Funding Information: The research of the fourth author is partially supported by KAKENHI 16K05102. The fifth author was partially supported by Simons Foundation grant #317096. The last author was supported by NSF grant DMS?1601024 and EPSCoR award OIA?1557417. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2020",
month = oct,
day = "15",
doi = "10.1016/j.jalgebra.2020.04.037",
language = "English",
volume = "560",
pages = "312--342",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}