Seminar
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| Location: | SLMath: Eisenbud Auditorium, Front Courtyard |
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Rational powers, invariant ideals, and the summation formula
Defined by Lejuene-Jalabert-Teissier and Huneke-Swanson, the rational powers of an ideal is a Q-filtration that contains the radical and the integral closure of the powers of the ideal. In this work we describe the rational powers and the Rees valuations of several classes of invariant ideals in terms of polyhedra. This allows us to show a summation formula for rational powers similar to Mustata's formula for multiplier ideals. Moreover, for arbitrary ideals over the complex numbers, we prove a weaker version of this formula that holds for sufficiently large rational numbers. This is joint work with Sankhaneel Bisui, Sudipta Das, and Huy Tai Ha.
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