The log canonical threshold and rational singularities

Cluckers, Raf; Mustata, Mircea; Kollár, János

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

The log canonical threshold and rational singularities

Author(s) :

Cluckers, Raf [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Mustata, Mircea [Auteur]
Kollár, János [Auteur]

Journal title :

Algebraic Geometry and Physics

Publisher :

International Press

Publication date :

2023

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

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, ...
Show more >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).Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2202.08425
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