Curves disjoint from a nef divisor

John Lesieutre, John Christian Ottem

Research output: Contribution to journalArticlepeer-review


On a projective surface it is well known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing an effective, nef line bundle on a threefold that is trivial on countably infinitely many curves. This answers a question of Totaro. As a pleasant corollary, we exhibit a quasi-projective variety with only a countably infinite set of complete, positive-dimensional subvarieties.

Original languageEnglish (US)
Pages (from-to)321-332
Number of pages12
JournalMichigan Mathematical Journal
Issue number2
StatePublished - Jun 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


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