Degree of the divisor of solutions of a differential equation on a projective variety

Details Degree of the divisor of solutions of a differential equation on a projective variety Degree of the divisor of solutions of a differential equation on a projective variety

1999-01-15

arxiv.org/abs/math/9901064v1

Mathematics

Algebraic Geometry

16 pages, Latex2e, uses diagrams package

Scientific paper

Using the data schemes developed by Arrondo-Sols-Speiser, we give a rigorous definition of algebraic differential equations on the complex projective space $P^n$. For an algebraic subvariety $S \subseteq P^n$, 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.

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