Details

Autor(en) / Beteiligte

• Zhu, Zhixian

Titel

Log canonical thresholds in positive characteristic

Ist Teil von

• Mathematische Zeitschrift, 2017-12, Vol.287 (3-4), p.1235-1253

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2017

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we study the singularities of pairs in arbitrary characteristic via jet schemes. For a smooth variety X in characteristic 0, Ein, Lazarsfeld and Mustaţǎ showed that there is a correspondence between irreducible closed cylinders and divisorial valuations on X . Via this correspondence, one can relate the codimension of a cylinder to the log discrepancy of the corresponding divisorial valuation. We now extend this result to positive characteristic. In particular, we prove Mustaţǎ’s log canonical threshold formula avoiding the use of log resolutions, making the formula available also in positive characteristic. As a consequence, we get a comparison theorem via reduction modulo p and a version of inversion of adjunction in positive characteristic.