Duality of the cones of divisors and curves

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Abstract

S. Payne asked whether for a variety X of dimension d, the closed cone spanned by the divisors ample in dimension k (1 ≤ k ≤ d) and the closed cone spanned by the classes of curves on some ℚ-factorial small modifications of X movable in codimension d - k are dual to each other. We prove that this is true for Fano type varieties and Mori dream spaces.

Original languageEnglish
Pages (from-to)403-416
Number of pages14
JournalMathematical Research Letters
Volume19
Issue number2
DOIs
Publication statusPublished - 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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