A new subadditivity formula for test ideals

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Smolkin, Daniel¹ 

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

关键词: F-singularities;    Test ideals;    Multiplier ideals;    Cartier algebras;    Toric varieties;   

DOI  :  10.1016/j.jpaa.2019.07.010

来源: Elsevier

【 摘 要 】

We exhibit a new subadditivity formula for test ideals on singular varieties using an argument similar to [9] and [16]. Any subadditivity formula for singular varieties must have a correction term that measures the singularities of that variety. Whereas earlier subadditivity formulas accomplished this by multiplying by the Jacobian ideal, our approach is to use the formalism of Cartier algebras [1]. We also show that our subadditivity containment is sharper than ones shown previously in [32] and [11]. The first of these results follows from a Noether normalization technique due to Hochster and Huneke. The second of these results is obtained using ideas from [33] and [11] to show that the adjoint ideal Jx (A, Z) reduces mod p to Takagi's adjoint test ideal, even when the ambient space is singular, provided that A is regular at the generic point of X. One difficulty of using this new subadditivity formula in practice is the computational complexity of computing its correction term. Thus, we discuss a combinatorial construction of the relevant Cartier algebra in the toric setting. (C) 2019 Published by Elsevier B.V.

【 授权许可】

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