Axial constants and sectional regularity of homogeneous ideals

Michael DeBellevue; Audric Lebovitz; Yik Li; Mohamed Lotfi; Shivam Mohite; Xin Pan; Mrigank Shekhar Pathak; Shah Roshan Zamir; Alexandra Seceleanu; Sindy Xin Zhang

Axial constants and sectional regularity of homogeneous ideals

Commutative Algebra 2022-08-03 v2

Authors: Michael DeBellevue , Audric Lebovitz , Yik Li , Mohamed Lotfi , Shivam Mohite , Xin Pan , Mrigank Shekhar Pathak , Shah Roshan Zamir , Alexandra Seceleanu , Sindy Xin Zhang

View on arXiv ↗ PDF ↗

Abstract

A notion of sectional regularity for a homogeneous ideal $I$ , which measures the regularity of its generic sections with respect to linear spaces of various dimensions, is introduced. It is related to axial constants defined as the intercepts on the coordinate axes of the set of exponents of monomials in the reverse lexicographic generic initial ideal of $I$ . The equivalence of these notions and several other homological and ideal-theoretic invariants is shown. It is also established that these equivalent invariants grow linearly for the family of powers of a given ideal.

Keywords

homogeneous ideals sectional regularity axial constants generic initial ideal reverse lexicographic order homological invariants

Cite

@article{arxiv.2110.13782,
  title  = {Axial constants and sectional regularity of homogeneous ideals},
  author = {Michael DeBellevue and Audric Lebovitz and Yik Li and Mohamed Lotfi and Shivam Mohite and Xin Pan and Mrigank Shekhar Pathak and Shah Roshan Zamir and Alexandra Seceleanu and Sindy Xin Zhang},
  journal= {arXiv preprint arXiv:2110.13782},
  year   = {2022}
}

Comments

Final version. To appear in PAMS

Axial constants and sectional regularity of homogeneous ideals

Abstract

Keywords

Cite

Comments

Related papers