Nonholomorphic Lefschetz fibrations with (-1)-sections

Noriyuki Hamada, Ryoma Kobayashi, Naoyuki Monden

Research output: Contribution to journalArticle

Abstract

We construct two types of nonholomorphic Lefschetz fibrations over S 2 with (-1)-sections-hence, they are fiber sum indecomposable-by giving the corresponding positive relators. One type of the two does not satisfy the slope inequality (a necessary condition for a fibration to be holomorphic) and has a simply connected total space, and the other has a total space that cannot admit any complex structure in the first place. These give an alternative existence proof for nonholomorphic Lefschetz pencils without Donaldson's theorem.

Original languageEnglish
Pages (from-to)375-398
Number of pages24
JournalPacific Journal of Mathematics
Volume298
Issue number2
DOIs
Publication statusPublished - Jan 1 2019

Keywords

  • (-1)-sections
  • Complex structure
  • Lefschetz fibrations
  • Slope inequality

ASJC Scopus subject areas

  • Mathematics(all)

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