An estimate for the F-pure threshold via the roots of the Bernstein-Sato polynomial

Abstract: Given a smooth complex algebraic variety X and a nonzero regular function f on X, I will describe an estimate for the difference between the log canonical threshold of f and the F-pure threshold of a reduction mod p of f, in terms of the roots of the Bernstein-Sato polynomial bf of f. This is based on some old work with S. Takagi and K.-i. Watanabe on one hand, and with W. Zhang on the other hand, plus one simple observation. Most of the talk will be devoted to an introduction to the invariants of singularities that feature in the result.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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