P^2中拟齐次曲线位形的对数向量场
Logarithmic vector fields for quasihomogeneous curve configurations in P^2
摘要：
设A是光滑平面曲线C_i的并，使得A的每个奇点是拟齐次的.证明了如果C是平滑曲线，使得A U C的每个奇点也是拟齐次的，则秩2丛存在初等修正，它将P^2上与A相切的向量场的O_{P^2}模Der（log A）与模Der（log A U C）联系起来.这就产生了一个研究丛Der（log A）和Der（log A U C）分裂的归纳工具，取决于除数A的几何形状|C在C上。
英文摘要：
Let A be a union of smooth plane curves C_i, such that each singular point of A is quasihomogeneous. We prove that if C is a smooth curve such that each singular point of A U C is also quasihomogeneous, then there is an elementary modification of rank two bundles, which relates the O_{P^2} module Der(log A) of vector fields on P^2 tangent to A to the module Der(log A U C). This yields an inductive tool for studying the splitting of the bundles Der(log A) and Der(log A U C), depending on the geometry of the divisor A|_C on C.
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