Integrability criteria for differential equations on the projective plane

نویسندگان

  • Javier Chavarriga
  • Dana Schlomiuk
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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تاریخ انتشار 2001