Mather discrepancy and the arc spaces
Abstract
The goal of this paper is a classification theorem of the singularities according to a new invariant, Mather discrepancy. On the other hand, we show some evidences convincing us that Mather discrepancy is a considerable invariant: By introducing new log-canonical threshold and minimal log-discrepancy by means of Mather discrepancy instead of usual discrepancy of canonical divisors, we obtain the formulas of the new log-canonical threshold in terms of arc spaces, inversion of adjunction for wider class of singularities than the known one, lower seimicontinuity of the new minimal log-discrepancy and the affirmative answer to a conjecture of Shokurov type; One advantage of the new invariants is that these are defined for arbitrary varieties (without q-Gorenstein property); These results include the known results for usual log-canonical threshold and minimal log-discrepancy.
Cite
@article{arxiv.1106.0345,
title = {Mather discrepancy and the arc spaces},
author = {Shihoko Ishii},
journal= {arXiv preprint arXiv:1106.0345},
year = {2012}
}
Comments
Some explanations are added in the proof of the main theorem. final version, to appear in Annales de l'Institut Fourier