On the BMY inequality on surfaces

TERZİ S.

COMMUNICATIONS IN ALGEBRA, vol.50, no.2, pp.714-725, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1080/00927872.2021.1967367
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.714-725
  • Keywords: BMY inequality, ordinarity, semistable fibrations
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we are concerned with the relation between the ordinarity of surfaces of general type and the failure of the BMY inequality in positive characteristic. We consider semistable fibrations pi : S -> C where S is a smooth projective surface and C is a smooth projective curve. Using the exact sequence relating the locally exact differential forms on S, C, and S/C, we prove an inequality relating c(1)(2) and c(2) for ordinary surfaces which admit generically ordinary semistable fibrations. This inequality differs from the BMY inequality by a correcting term which vanishes if the fibration is ordinary.