Betti numbers of symmetric shifted ideals
Commutative Algebra
2020-10-29 v5 Combinatorics
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
Cite
@article{arxiv.1907.04288,
title = {Betti numbers of symmetric shifted ideals},
author = {Jennifer Biermann and Hernán De Alba and Federico Galetto and Satoshi Murai and Uwe Nagel and Augustine O'Keefe and Tim Römer and Alexandra Seceleanu},
journal= {arXiv preprint arXiv:1907.04288},
year = {2020}
}
Comments
Corrected typo in Example 5.8