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Rational powers, invariant ideals, and the summation formula

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arxiv 2402.12350 v3 pith:N2J4FPRQ submitted 2024-02-19 math.AC

Sankhaneel Bisui , Sudipta Das , Tài Huy Hà , Jonathan Montaño This is my paper
classification math.AC
keywords idealsrationalformulapowersholdsinvariantsummationversion
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We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear groups, in terms of polyhedra and lattice points. This allows us to show that a version of Musta\c{t}\u{a}-Takagi's summation formula for multiplier ideals also holds for the rational powers of these ideals. Moreover, for arbitrary ideals in normal domains that are finitely generated over algebraically closed fields, we prove a weaker version of this formula that holds for sufficiently large rational numbers.

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  1. Degree functions of graded families of ideals

    math.AC 2025-06 conditional novelty 6.0 of 10

    Multiplicities and degree functions of graded families of ideals are expressed as limits of intersection products, with a closed formula for Q-divisorial filtrations in dimension 2.

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