Integrability criteria for differential equations on the projective plane
نویسندگان
چکیده
In this article we prove two new criteria for the existence of rational general integral of an algebraic differential equation (cf. [4]) on the complex projective plane. These results are stated in terms of divisors and zero-cycles of a projective variety and are built by using intersection numbers of projective curves and multiplicities of singularities. We also prove a new result giving new sufficient conditions for the existence of a Darboux general integral for quadratic differential equations over the projective plane.
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