A Note on the Strict Transformation of an Effective Cartier Divisor

2023/04/19 by Zhao, Yu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.09475

Abstract

Let Y be an effective Cartier divisor of a smooth variety Z. Let X_i, i∈ \1,⋯,n\ be a set of pairwise disjoint smooth subvarieties in Y such that their union contains the singular locus of Y. In this paper, we give a sufficient condition such that Bl_XY is smooth, where X is the disjoint union of all X_i. Moreover, we prove that assuming a dimensional condition, there is an admissible subcategory of D^b(Bl_XY) which is a weak categorical crepant resolution of Y in the sense of Kuznetsov.

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