Mathematical Research Letters

Volume 19 (2012)

Number 2

Duality of the cones of divisors and curves

Pages: 403 – 416

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n2.a12

Author

Sung Rak Choi

Abstract

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.

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