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

arXiv · 2110.13782

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

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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.

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Michael DeBellevue, Audric Lebovitz, Yik Li, Mohamed Lotfi, Shivam Mohite, Xin Pan, Mrigank Shekhar Pathak, Shah Roshan Zamir, Alexandra Seceleanu, Sindy Xin Zhang. 2021-10-26. Axial constants and sectional regularity of homogeneous ideals. https://arxiv.org/abs/2110.13782

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