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- W2912804492 abstract "We show that if f is a nonzero, noninvertible function on a smooth complex variety X and J_f is the Jacobian ideal of f, then lct(f, J_f^2)>1 if and only if the hypersurface defined by f has rational singularities. Moreover, if this is not the case, then lct(f, J_f^2)=lct(f). We give two proofs, one relying on arc spaces and one that shows that the minimal exponent of f is at least as large as lct(f, J_f^2). In the case of a polynomial over the algebraic closure of Q, we also prove an analogue of this latter inequality, with the minimal exponent replaced by the motivic oscillation index moi(f)." @default.
- W2912804492 created "2019-02-21" @default.
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- W2912804492 date "2020-11-24" @default.
- W2912804492 modified "2023-10-17" @default.
- W2912804492 title "An invariant detecting rational singularities via the log canonical threshold" @default.
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