Mather discrepancy and the arc spaces

Details Mather discrepancy and the arc spaces Mather discrepancy and the arc spaces

2011-06-02

arxiv.org/abs/1106.0345v2

Mathematics

Algebraic Geometry

Some explanations are added in the proof of the main theorem. final version, to appear in Annales de l'Institut Fourier

Scientific paper

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.

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