On Lotka-Volterra Foliation On The Projective Plane

The invariants of foliation are important tool for the study of birational geometry of foliations.Sheng-Li Tan[44]introduce three important invariants of surface foliations.In order to study the problem of geography of these invariants,we need many examples,but now we know little examples,and know little about the geography problem.So it's essential to compute these invariants of many different classical foliationsThis dissertation studies the invariants of LotKa-Volterra foliations.Concretely saying.we mainly solve the following three problems(1)Classify Lotka-Volterra foliation under the projective equivalent into 11 classes(2)Compute the invariants of foliations defined by equations(?)-(?),(?)-(?);When pa- rameters satisfy some explicit conditions,and compute some invariants of other foliations(3)Study the problem of geography about these invariantsThe difficulty of the study is how to calculate the negative part of Zariski decomposition for the canonical divisor of foliation(may not be relatively minimal)explicitly.We solve this difficulty in conditions.We make full use of many classical techniques of algebraic surfaces and foliation to solve this problem,and combine these methods in our disscussion,it's a characteristic of this article...