Grauert-Riemenschneider multiplier ideal sheaves and the (optimal) Briançon-Skoda number

2021/04/28 by Li, Zhenqian
#13B22 #14F18 #32B05 #32S05 #32U05 #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.14047

Abstract

The goal of this note is to survey some recent results on the Grauert-Riemenschneider multiplier ideal sheaves on any (reduced) complex space of pure dimension. In particular, we obtain the Briançon-Skoda number for any Noetherian ring of weakly holomorphic functions with weakly rational singularities (not essentially of finite type over ℂ and Cohen-Macaulay local rings), which will partially answer a question of Huneke.

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