We consider the blowup X(a, b, c) of a weighted projective space \({\mathbb {P}}(a,b,c)\) 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 \(\chi ({\mathcal {O}}_X(C))\). 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.

中文翻译：

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Mori 梦想的加权投影平面爆炸

我们考虑加权射影空间\({\mathbb {P}}(a,b,c)\)在一般非奇异点的放大X ( a ,  b ,  c ) 。我们根据\(\chi ({\mathcal {O}}_X(C))\)给出了曲线是X ( a ,  b ,  c )上的负曲线的充分条件。这可以用于找到X ( a ,  b ,  c )的有效锥体，并且可以作为证明许多加权投影平面爆炸的 Mori 梦想的起点。确认某某X的森梦(a ,  b ,  c ) 作为我们方法的例子。