Higher Jacobian ideals, contact equivalence and motivic zeta functions

• Quy Thuong Lê ^[2] ; Takehiko Yasuda ^[1]
  1. [1] Osaka University

     Osaka University

     Kita Ku, Japón

     
  2. [2] Vietnam National University, Hanoi, Vietnam; Osaka University, Osaka, Japan
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 41, Nº 3, 2025, págs. 1057-1080
• Idioma: inglés
• DOI: 10.4171/RMI/1516
• Enlaces
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• Resumen

  • We show basic properties of higher Jacobian matrices and higher Jacobian ideals for functions and apply it to obtain two main results concerning singularities of functions. Firstly, we prove that a higher Nash blowup algebra is invariant under contact equivalences, which was recently conjectured by Hussain, Ma, Yau and Zuo. Secondly, we obtain an analogue of a result on motivic nearby cycles by Bussi, Joyce and Meinhardt