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Degree of the divisor of solutions of a differential equation on a projective variety |
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| Authors: | Vicente Muñoz Ignacio Sols |
| Institution: | 1. Departamento de álgebra Geometría y Topología Facultad de Ciencias , Universidad de Málaga , Campus de Teatinos, Malaga, 29071, Spain E-mail: mailto:vmunoz@agt.cie.uma.es;2. Departamento de álgebra Facultad de Ciencias Matematicas , Universidad Complutense de Madrid , Madrid, 28040, Spain E-mail: mailto:sols@mat.ucm.es |
| Abstract: | Using the data schemes from 1] we give a rigorous definition of algebraic differential equations on the complex projective space Pn. For an algebraic subvariety S?Pn, we present an explicit formula for the degree of the divisor of solutions of a differential equation on S and give some examples of applications. We extend the technique and result to the real case. |
| Keywords: | Primary: 14D20 Secondary: 14D20 Secondary: 14M15 Secondary: 14P05 |