Adjoint ideals and a correspondence between log canonicity and F-purity
Abstract
This paper presents three results on F-singularities. First, we give a new proof of Eisenstein's restriction theorem for adjoint ideal sheaves, using the theory of F-singularities. Second, we show that a conjecture of Musta\c{t}\u{a} and Srinivas implies a conjectural correspondence of F-purity and log canonicity. Finally, we prove this correspondence when the defining equations of the variety are very general.
Keywords
Cite
@article{arxiv.1105.0072,
title = {Adjoint ideals and a correspondence between log canonicity and F-purity},
author = {Shunsuke Takagi},
journal= {arXiv preprint arXiv:1105.0072},
year = {2013}
}
Comments
23 pages, v2: Introduction revised, Section 2 expanded (Example 2.9 and Remarks 2.6, 2.8 and 2.12 added), new references added, no other substantial changes, v3: an error in the proof of Theorem 2.10 of the previous version corrected, v4: an error in Example 2.10 corrected, other minor changes, to appear in Algebra Number Theory, v5: an error in the proof of Theorem 2.11 fixed