Duality of the cones of divisors and curves

Sung Rak Choi

Research output: Contribution to journal › Article

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

Choi, Sung Rak. / Duality of the cones of divisors and curves. In: Mathematical Research Letters. 2012 ; Vol. 19, No. 2. pp. 403-416.
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Choi, SR 2012, 'Duality of the cones of divisors and curves', Mathematical Research Letters, vol. 19, no. 2, pp. 403-416. https://doi.org/10.4310/MRL.2012.v19.n2.a12

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 journal › Article

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AB - 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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Choi SR. Duality of the cones of divisors and curves. Mathematical Research Letters. 2012;19(2):403-416. https://doi.org/10.4310/MRL.2012.v19.n2.a12

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