Duality of the cones of divisors and curves

Research output: Contribution to journalArticle

5 Citations (Scopus)

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

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Divisor
Duality
Cone
Closed
Curve
Factorial
Codimension
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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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.",
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Duality of the cones of divisors and curves. / Choi, Sung Rak.

In: Mathematical Research Letters, Vol. 19, No. 2, 2012, p. 403-416.

Research output: Contribution to journalArticle

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