On the behavior of singularities at the $F$-pure threshold
Commutative Algebra
2019-06-25 v3 Algebraic Geometry
Abstract
We provide a family of examples where the -pure threshold and the log canonical threshold of a polynomial are different, but where does not divide the denominator of the -pure threshold (compare with an example of \mustata-Takagi-Watanabe). We then study the -signature function in the case where either the -pure threshold and log canonical threshold coincide or where does not divide the denominator of the -pure threshold. We show that the -signature function behaves similarly in those two cases. Finally, we include an appendix which shows that the test ideal can still behave in surprising ways even when the -pure threshold and log canonical threshold coincide.
Cite
@article{arxiv.1508.05427,
title = {On the behavior of singularities at the $F$-pure threshold},
author = {Eric Canton and Daniel Hernández and Karl Schwede and Emily Witt and Alessandro De Stefani and Jack Jeffries and Zhibek Kadyrsizova and Robert Walker and George Whelan},
journal= {arXiv preprint arXiv:1508.05427},
year = {2019}
}
Comments
Typos corrected, other improvements to the exposition