Effective cones of cycles.pdf (433.79 kB)
Download fileEffective Cones of Cycles on Blow-ups of Projective Space
journal contribution
posted on 2017-01-19, 00:00 authored by Izzet Coskun, John Lesieutre, John Christian OttemIn 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.