Abstract
AbstractWe consider the blowup X(a, b, c) of a weighted projective space $${\mathbb {P}}(a,b,c)$$
P
(
a
,
b
,
c
)
at a general nonsingular point. We give a sufficient condition for a curve to be a negative curve on X(a, b, c) in terms of $$\chi ({\mathcal {O}}_X(C))$$
χ
(
O
X
(
C
)
)
. This can be applied to find the effective cone of X(a, b, c) and can serve as a starting point to prove the Mori dreamness of blowups of many weighted projective planes. We confirm the Mori dreamness of some X(a, b, c) as examples of our method.
Funder
Western Norway University of Applied Sciences
Publisher
Springer Science and Business Media LLC
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