TY - JOUR

T1 - Effective cones of cycles on blowups of projective space

AU - Coskun, Izzet

AU - Lesieutre, John

AU - Ottem, John Christian

N1 - Publisher Copyright:
© 2016 Mathematical Sciences Publishers.

PY - 2016

Y1 - 2016

N2 - 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 Xnr of ℙn, n > 4 at r very general points, the cone of divisors is not finitely generated as soon as r > n C3, whereas the cone of curves is generated by the classes of lines if r ≤2n. In fact, if Xnr is a Mori dream space then all the effective cones of cycles on Xnr are finitely generated.

AB - 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 Xnr of ℙn, n > 4 at r very general points, the cone of divisors is not finitely generated as soon as r > n C3, whereas the cone of curves is generated by the classes of lines if r ≤2n. In fact, if Xnr is a Mori dream space then all the effective cones of cycles on Xnr are finitely generated.

UR - http://www.scopus.com/inward/record.url?scp=85002045594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85002045594&partnerID=8YFLogxK

U2 - 10.2140/ant.2016.10.1983

DO - 10.2140/ant.2016.10.1983

M3 - Article

AN - SCOPUS:85002045594

SN - 1937-0652

VL - 10

SP - 1983

EP - 2014

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 9

ER -