Pathologies and liftability of Du Val del Pezzo surfaces in positive characteristic

Tatsuro Kawakami, Masaru Nagaoka

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we study pathologies of Du Val del Pezzo surfaces defined over an algebraically closed field of positive characteristic by relating them to their non-liftability to the ring of Witt vectors. More precisely, we investigate the condition (NB): all the anti-canonical divisors are singular, (ND): there are no Du Val del Pezzo surfaces over the field of complex numbers with the same Dynkin type, Picard rank, and anti-canonical degree, (NK): there exists an ample Z-divisor which violates the Kodaira vanishing theorem for Z-divisors, and (NL): the pair (Y, E) does not lift to the ring of Witt vectors, where Y is the minimal resolution and E is its reduced exceptional divisor. As a result, for each of these conditions, we determine all the Du Val del Pezzo surfaces which satisfy the given one.

Original languageEnglish
Pages (from-to)2975-3017
Number of pages43
JournalMathematische Zeitschrift
Volume301
Issue number3
DOIs
Publication statusPublished - Jul 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

Fingerprint

Dive into the research topics of 'Pathologies and liftability of Du Val del Pezzo surfaces in positive characteristic'. Together they form a unique fingerprint.

Cite this