向量场、不变簇与线性系
Vector Fields, Invariant Varieties and Linear Systems
摘要：
研究了向量场的不变簇与线性系关于向量场的拐点轨迹之间的相互作用。在这样的调查的后果，我们得到了一个计算标准的存在合理的首次积分的一个给定的程度，界的首次积分的家庭的向量场和推广的达布的标准。我们还对Gomez-Mont关于所有叶代数的叶理的结果给出了一个新的证明。
英文摘要：
We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criteria for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields and a generalization of Darboux's criteria. We also provide a new proof of Gomez-Mont's result on foliations with all leaves algebraic.
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