Izzet Coskun, John Lesieutre and John Christian
Ottem
Vol. 10 (2016), No. 9, 1983–2014
DOI: 10.2140/ant.2016.10.1983
Abstract
In this paper we study the cones of higher codimension (pseudo)effective cycles on point
blowups 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 blowup
of
,
at
very general points, the cone of divisors is not finitely generated as soon as
,
whereas the cone of curves is generated by the classes of lines if
. In fact,
if
is a Mori dream space then all the effective cones of cycles on
are
finitely generated.
Keywords
Cones of effective cycles, higher codimension cycles,
blowups of projective space, Mori dream space