Effective Cones of Cycles on Blow-ups of Projective Space
Ottem, John Christian
PublisherMathematical Sciences Publishers
MetadataShow full item record
In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for which these cones are finitely generated. Surprisingly, we discover that for (very) general points, the higher codimension cones behave better than the cones of divisors. For example, for the blow-up Xn r of P n, n > 4, at r very general points, the cone of divisors is not finitely generated as soon as r > n + 3, whereas the cone of curves is generated by the classes of lines if r ≤ 2 n. In fact, if Xn r is a Mori Dream Space then all the effective cones of cycles on Xn r are finitely generated.
SubjectCones of effective cycles
higher codimension cycles
blow-ups of projective space