NOTIONS OF NUMERICAL IITAKA DIMENSION DO NOT COINCIDE

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Abstract

Let X be a smooth projective variety. The Iitaka dimension of a divisor D is an important invariant, but it does not only depend on the numerical class of D. However, there are several definitions of “numerical Iitaka dimension”, depending only on the numerical class. In this note, we show that there exists a pseuodoeffective R-divisor for which these invariants take different values. The key is the construction of an example of a pseudoeffective R-divisor D+ for which h0(X, ⌊mD+⌋ + A) is bounded above and below by multiples of m3/2 for any sufficiently ample A.

Original languageEnglish (US)
Pages (from-to)113-126
Number of pages14
JournalJournal of Algebraic Geometry
Volume31
Issue number1
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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