Multiplier ideal sheaves, jumping numbers, and the restriction formula

Abstract

In the present article, we establish an equality condition in the restriction formula on jumping numbers by giving a sharp lower bound of the dimension of the support of a related coherent sheaf. As applications, we obtain equality conditions in the restriction formula on complex singularity exponents by giving the dimension, the regularity and the transversality of the support, and we also obtain some sharp equality conditions in the fundamental subadditivity property on complex singularity exponents. We also obtain two sharp relations on jumping numbers.

26 pages. For the sake of the entirity and contiuity of the content, we strengthen the main results in arXiv:1510.03586, and combine arXiv:1510.03586 with the present manuscript

References in corpus (4)

• Effectiveness of Demailly's strong openness conjecture and related problems
• Strong openness conjecture for plurisubharmonic functions
• Extension of holomorphic functions defined on non reduced analytic subvarieties
• Strong openness conjecture and related problems for plurisubharmonic functions

Cited by in corpus (4)

• General concavity of minimal $L^2$ integrals related to multiplier ideal sheaves
• Log canonical thresholds and Monge-Ampere masses
• Multiplier ideal sheaves with weights of log canonical threshold one
• Multiplier ideal sheaves, complex singularity exponents, and restriction formula