Briançon-Skoda exponents and the maximal root of reduced Bernstein-Sato polynomials

Seung-Jo Jung ^[3] ; In-Kyun Kim ^[1] ; Morihiko Saito ^[4] ; Youngho Yoon ^[2]
1. [1] Yonsei University
  
  Yonsei University
  
  Corea del Sur
2. [2] Chungbuk National University
  
  Chungbuk National University
  
  Corea del Sur
3. [3] Jeonbuk National University, Korea
4. [4] RIMS Kyoto University, , Japan
Mostrar afiliaciones +
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 4, 2022
Idioma: inglés
Enlaces
- Texto completo (pdf)
Resumen
- For a holomorphic function f on a complex manifold X, the Briançon-Skoda exponent eBS( f ) is the smallest integer k with f k ∈ (∂ f ) (replacing X with a neighborhood of f −1(0)), where (∂ f ) denotes the Jacobian ideal of f . It is shown that eBS( f ) ≤ dX (:= dim X) by Briançon-Skoda. We prove that eBS( f ) ≤ [dX −2α f ]+1 with −α f the maximal root of the reduced Bernstein-Sato polynomial b f (s)/(s + 1), assuming the latter exists (shrinking X if necessary). This implies for instance that eBS( f ) ≤ dX −2 in the case f −1(0) has only rational singularities, that is, if α f > 1.