Mathematical Research Letters
Volume 19 (2012)
Duality of the cones of divisors and curves
Pages: 403 – 416
S. Payne asked whetherfor a variety $X$ of dimension $d$, the closed cone spanned by thedivisors ample in dimension $k$ ($1\leq k\leq d$) and the closed conespanned 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.